steve-and-alice-realized-that-their-ages-are-consecutive-odd-integers-the-product-of-their-ages-is-1

Name: steve and alice realized that their ages are consecutive odd integers the product of their ages is 1
Uploaded: 2020-05-01
Duration: 4 min 20 s
Channel: Numerade
Description: Steve and Alice realized that their ages are consecutive odd integers. The product of their ages is $195 .$ Steve is younger than Alice. Determine their ages by completing the square.

Question

Steve and Alice realized that their ages are consecutive odd integers. The product of their ages is $195 .$ Steve is younger than Alice. Determine their ages by completing the square.

Foster Wisusik · Accepted Answer

Okay. This question concerns the ages of two people. So Steve and Alice have ages that air Consecutive odd integers. So what does that mean? Well, consecutive odd integers like one and three more seven and nine are of the form to K minus one and two K plus one. So it says that the product of two of these odd consecutive energy rages are 1 95 So 1 95 equals to K minus one times two K plus one. And I&#x27;m not just using any intruders here because they have to be odd. That&#x27;s why we have this two K minus one. Because that&#x27;s the form of an odd number because two K is the form of uneven number. So we subtract one to get the form of a not number or doing this out. We get four k squared minus tu que plus two K minus one equals 1 95 and we can simplify this as four K squared minus one equals 1 95 or four K squared minus 1 96 equals zero. And actually, what we can do is pull out of four to get four times K squared minus 1 96 Divided by four. Wish we could do the math on this real fast. Cols And in 19 4 times with remainder three so 49 k squared minus 49 is equal to zero. And this four has nothing to do with our situation. So you can just cancel it because it&#x27;s not gonna make cake with zero. It&#x27;s not gonna make this expression equal to zero. Rather, so we know that K squared has to equal 49 and, well, okay can either be positive or negative seven. But we&#x27;re dealing with positive numbers because we&#x27;re dealing with age streaky. Cut off that K value. So now, looking back to the very beginning, we said that Steve is younger than Alice. So Steve has aged to K minus one, and Alice is older by two years. So her age is two K plus one. So if we plug in K equals seven for each of these, Steve is 14 minus one, which is 13 and Alice is 14 plus one, which is 15. And just like that, we&#x27;ve solved for each person&#x27;s age

Harsh Gadhiya · Answer

way are given to the product of two consecutive and teachers. Let them be X and X plus one is 19 more than there, some so x multiplied by X plus one is equal to X plus X plus one plus 19 or this is X square plus eggs is equal toe do X plus 20 I bring this to the other side. This is X squared minus X minus 20 is equal to zero. I can break this as minus five and plus four plus four minus five multiplied by plus four is minus 20. So this is going to be X square minus four SRE plus four X minus five X minus with zero Heidi excess common. So this is X plus four minus favors common and X plus four again is equal to zero. This gives me two solutions. First one is X is equal to five and the other one is X is equal to minus four. We were here from this one. I get my pair off in teachers X X and X plus one. So this is five Hamas six. And from here I get minus four comma minus three. These are our answers

Deboney Harris · Answer

All right. So we need to find two numbers whose product equal 90. So when you multiply them together x times y equal 90. And when you add or have the sum of their squares, it&#x27;s gonna equal to 61. So you have one number squared, plus the other number squared. Is it getting equal to 61 so we can solve this using the substitution method by solving for X or Y in our first equation? I&#x27;m just gonna divide by Why on both sides making my X equal 90 over Why? And I can just plug that into my second equation here. So I&#x27;m gonna have 90 over Why Squared Plus y squared equals 2 61 Let&#x27;s go ahead and square inside those parentheses so we can have 8100 over Why Squared plus y squared equals 2 61 And let&#x27;s go ahead and multiply out that Why squared so that we don&#x27;t have that fraction anymore is gonna cancel that out. So I don&#x27;t have 8100 plus y squared equals 2 61 y squared. Or that&#x27;s why did 1/4 equals 2 61 I swear. There we go. Go ahead and get everything on the same set of our equation by minus sing or subtracting by to 61 squared on both sides. Then we&#x27;re gonna have a wider the fourth minus 2 61 Why squared? Plus aiding on 100. Now we can go ahead and factor this out, so we&#x27;re gonna have a y squared. Why squared? We need to find two squares when multiplied together equal 8100 when added equal to 61. Well, if we have 36 times 2 25 is gonna equal 8100. Add those together. Those equal to 61 those are both swears. Want them to be negatives. Because a native tens of negative is a positive and once attracted still gonna be a negative. So let&#x27;s go ahead and expand that out. Ah, Why? Minus six. Why plus six is gonna get us are y squared minus 36. And why minus 15? Why plus 15 is going to get us are y squared minus 2 25 Now, if we saw all of those wise equal to zero are why is gonna be equal to positive six. Negative six. Positive 15 and negative 15 and let&#x27;s go ahead and plug. Listen to our ex equation to figure out what are X is gonna be in those situations so our X is equal to 90. Divided by six. That&#x27;s 15 x equal to 90 divided by negative six. That&#x27;s negative. 15. X equals 90 Divided by 15 It&#x27;s gonna be six. X equals 90 divided by negative 15. It&#x27;s gonna be negative. Six. Suck when our ex is 15 hour. Why is six when our ex is negative? 15 hour. Why is negative six When our X is positive, six are wise 15 They&#x27;re X is negative six hour. Why is negative team? Here are the possible numbers that we could use in this scenario.

Ankit Gupta · Answer

according to the ocean, we will that even Gonzi Q T numbers duties X minus two eggs X plus. Cool according to the cushion when we used caution. Doctor Vol. X Plus two Whole scare is equal to 76 plus ex scwill, then the soul. This equation. We know that views a plus. The whole school identity when we use there is X Square plus four plus four. X is equal to 76 plus x scwill. When we sold this equation, we have four. X is equal toe 72. The value of X comes out there is 18. We know that we lack even consecutive Tom X minus two x x plus two. The value off consecutive terms comes out. There is 16 18 and 20 when we put value of X is 18 their first consecutive film, X minus two. We have 16 and X is eating, and X plus two is 20

Heather Zimmers · Answer

okay. And this problem, we&#x27;re finding two consecutive integers that meet certain requirements. Consecutive imagers would be integers in a row like five and 6 10 and 11 Negative nine and negative A something like that. So let&#x27;s call them X and X plus one. Okay, we know this. Some of their squares is 61 so the sum of their squares is what you get. If you square each one x squared, X plus one squared and then you add those. So the sum of the squares is equal to 61. So there&#x27;s our equation. We&#x27;re going to solve it for X, so the first thing we need to do is square the X Plus one. So we have to use the foil technique X plus one times X plus one. And that&#x27;s going to give us for that part of the equation. X squared plus two x plus one. And let&#x27;s go ahead and combine our like terms. So we have two x squared plus two x plus one. Let&#x27;s subtract 61 from both sides, so now we have minus 60 equals zero. Let&#x27;s divide the whole equation by two to make everything easier to work. with. And now let&#x27;s see if this factors so we could try X plus six and X minus five. Those would multiply to give us negative 30 and they add to one. So that looks good. So we set each factor equal to zero, and then we solve each one and we get X equals negative. Six. We get X equals five. So that means one answer combination could be that the consecutive integers are negative. Six and the next one up at 12 it would be negative. Five four. If X is five, add one to it. The next one up would be six. So our answer is either negative six. Negative five or positive five. Positive six.

Ankit Gupta · Answer

Lector or number Thanks if one or numerous eggs we know the difference between two consecutive or numbers is too. So next Con Security all number express Do so according to the question, We have the product off two consecutive on the bus Doctors expected, like express school equal 62. We can for this. And if I decide to explore plus two x minus 63 equals zero for the begin guide decides X good. Yes, my next minus seven. It&#x27;s minus 62 equals zero. For that we can t the common terms so we can fight this as eggs Medic Like that expressed name minus seven. My Life Express nine equals zero Here we can now form the two factors as X plus nine I X minus seven liquid zero. Now we can equate this factory boosters either. So we get X Plus nine equals zero or X minus seven equals zero from express 19. Good zero. We get X equal minus nine and from X minus seven. Quit receiver. We get X equal seven from here. What? We get this it is x equal minus nine, Then next Corns acute our number minus 90 plus food equals minus seven on. So it&#x27;s at secret to seven. Then next cause acute. Our number will be seven plus two doctors night.

Problem 37 Hard Difficulty

Steve and Alice realized that their ages are consecutive odd integers. The product of their ages is $195 .$ Steve is younger than Alice. Determine their ages by completing the square.

Answer

The 2 numbers are 13 and $15 .$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Grace H.

Anna Marie V.

Heather Z.

Maria G.

Absolute Value - Example 1

Absolute Value - Example 2

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The 2 numbers are 13 and $15 .$

Algebra 2 and Trigonometry

Grace H.

Anna Marie V.

Heather Z.

Maria G.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Grace H.

Anna Marie V.

Heather Z.

Maria G.

Ann Xavier Gantert

Algebra 2 and Trigonometry