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Question

Solve each problem by using a system of three equations in
three unknowns.

Harry has 2.25 dollars in nickels, dimes, and quarters. If he had twice as many nickels, half as many dimes, and the same number of quarters, he would have 2.50 dollars . If he has 27 coins altogether, then how many of each does he have?

Jake Zanazzi · Accepted Answer

to your given another coin problem. We&#x27;re told that the value of nickels, times quarters, make little case for consistency equals two hours, according other scents. And we&#x27;re told that if he has doubles the amount of nickel half the amount of times you see, you have a $2.50 more gold cult member coins seven should be que here some of equations that can. Because I saw what we saw this using elimination for 25 year point of life here, one here. So it should be pretty easy to eliminate. Do that cop, um, pressed equation minus the second equation. When you get minus point of Bob and plus point over the equals minus 0.5. Man, we take this first equation multiplied by four. The second equation you do with the most black 54. A second reason, most about four. Quick for and plus point two d los que Those 10. Now, if we take this, it&#x27;s this. So I subtract the first equation. You have minus 0.6 on the minus seven people. Right now, we have two equations to another&#x27;s, um, and we can solve if we, um multiply this top equation by 20 we&#x27;re gonna get negative and plus the course point for five times 20. Just gonna be thought it was negative. Now we&#x27;re gonna have e equals And I&#x27;m five and we complain that in seclusion right here and months it&#x27;s going to give us negative 0.6 and mind quite it. And plus five is gonna before I think some 13. I mean, negative. So negative. 1.4 and one and it&#x27;s gonna be toiling about four friends. Gonna equal this. Want that n equals 15. We know that e equals the U minus. Far gonna be cat. I only know the q equals the seven minus and minus d just gonna equal to. So we have a number of nickels. Times quarters is gonna equal 15 can to

Jake Zanazzi · Answer

So this is a money question. We know that this person has dimes, Nichols quarters, and in total, he is 13 coins. So then we&#x27;re told that the total value of the coins, which just point 10 times D those porno five comes and because 0.25 times q equals 1 75 Finally, we&#x27;re told the number of times it was two times the number of vehicles. So now we have to, um, you substitution here and solved. We can plug in to end for D here, so it&#x27;s gonna be three. And what&#x27;s Q equals 13 between q equals 13 minus three. And now we have every variable in terms of the end. So complected into our final equation to salt 0.1 comes to an end plus point of five and close 50.25 irking minus three and 1 75 So now we&#x27;re gonna have a point to and five and plus 0.25 times 13 3 25 by this point in five times three minus 30.75 and 1 75 So now you 0.25 minus 0.75 So we have my point black and equals 1 75 minus 3 20 minus 1.5. And it&#x27;s gonna equal three. Once we solve for n equals three, we can solve quickly or d he&#x27;s gonna equal six. Q is gonna be 13 minus three comes three be four. So we know the number of guys nickels and quarters gonna equal six. Three for we can plug this back, then to make sure, um, that this solution works.

Julie Silva · Answer

So in this problem, we want to figure out how many coins of each type does when Warren half while the two clips of coins he has their dimes and nickels. So let&#x27;s d represent how many times he has. And let&#x27;s end represent how Maney Nichols. Yes, well, we&#x27;re told he has 35 total coins. Some. When we add up the number of times which is d plus the number, and Nichols, which is n it should equal 35. Now we&#x27;re told the value of his coins is $3.30. Well, remember, a dine is worth 10 cents, so 0.10 d represents the total value he&#x27;ll have in dimes and nickels were five cents. So 0.5 n represents the total value of his vehicles. And we know in total it should equal to $3.30. So now we have our system of equation, and you can solve by even method, addition, method or substitution. I&#x27;m going to use the addition. Nothing. So I&#x27;m to do that. I&#x27;m gonna multiply the first equation by negative 0.10 So negative 0.10 times D is negative. 0.20 negative, 0.10 times n is negative, 0.10 and and then when you multiply negative 0.10 times 35 we&#x27;re gonna get negative 3.5. So now we can go ahead and add the two equations because 20.10 D minus 0.20 cancels. Well, then we have 0.5 n minus 0.10 in, which is going to be negative 0.5 and then we have 3.30 minus 3.5, which is negative 0.2. So now we just have to divide both sides of our equation by negative 0.5 And so what we&#x27;re gonna find when we do in negative 0.2 divided by negative 0.5 we&#x27;re going to get four, which means he has four nickels. Now we just have to figure out how many times he has. So I&#x27;m going to do this by going back to the first equation. De plus en is 35 and we know and is four. So D plus fours 35. So when we subtract four from both so that both sides or the find D is 31 so he has 31 times and four nickels

Ashley Volpe · Answer

Okay, so we&#x27;re dealing with some quarters and Dom&#x27;s, and it tells us that we have the number of quarters and dimes put together. We have 39 coins. It also talks about the value of these coin, and we know that each quarter we own cost 25 cents or is worth 25 cents. We know that each dime is worth 10 cents, and then his money total was $7.50. So I have my system of equations I need to solve going to solve by using elimination. So I&#x27;m going to multiply this top one by 10.10 That&#x27;s gonna give me 0.10 Q plus 0.10 d equals three point. Now that I&#x27;ve done that, I have a system here where I can subtract, and when I subtract this, I get 0.1 Q equals 3.6, dividing by 0.15 then leads me to Q equal to 24. Since the number of coins have is 39 that&#x27;s going to mean that 24 plus d equals 39 and so the number of dimes I have been subtracting 24 is 15. So I have 24 quarters and 15 times in this situation

Mrinal Rana · Answer

so, firstly, in the question, it says there are five more dimes and quarters, so I&#x27;m gonna have why equals Explosive Fi? And also it says nine more nickels and quarters. The number of nickels is nine more than the quarters, and the next they conform my equation. Joe quantify explosive 0.1 by plus, Still going to I said you called 2.75 second substitute These into the main equation toe have just one unknown. So, uh, X plus five. Plus, you&#x27;re a bunch of by X plus nine equals 3.75 So this is gonna be through one X plus your one stop one show five x plus sarah 0.45 equals 3.75 So I added up all the ex terms, I&#x27;m gonna have 0.25 point 35 0.4 x and 0.5 on the left side. Subtract that on the right side to get 3.25 and so x is gonna equal are sorry. I made a mistake here. This is actually going to be 3.75 minus 145 plus 0.5 is your 0.95 and now ex is gonna be point being divided by you&#x27;re going for just seven. You got 7/4. Why is exposed by which is seven plus 5 to 12? Uh, dimes that is exposed. Nine. So seven plus nine, which is are nine, which is 16 Nichols.

Wesley Hines · Answer

So we&#x27;re trying to find out, um, the combination of coins that Emma used, given the price, um, of the lunch and another constraints. So winds and Mark X Y Z for ex being pennies. Why being Nichols? Okay, legal Anzi being dimes. So we&#x27;re given that she used 232 coins. That means that X is equal to X plus y plus See, that&#x27;s equal to 232. And we&#x27;re also given that&#x27;s the number of nickels. Plus, the number of dimes was equal to the number of pennies. So that tells us that X is equal to why pussy. And then we&#x27;re also told that the total bill was 10 36 Well, if a penny&#x27;s 360.11 sense a Nicholas five cents and the time is 10 cents, well, then 0.1 exposed 0.5 wine plus 0.1 Z should equal 10. 36. So, using this system, we need to solve for the three the three equations. Now, one thing we can note right away this is kind of a gimme. Um, is that why? Plus Z is equal to X? Well, that means that half the coins or pennies. So we know right away that excess 116 as that&#x27;s half of to 32. We could do this mathematically by, uh, we know here that X is equal to y plus c so because substitute this y plus c with an axe center, we get two X. He was 2 32 But just off the word problem, we confer that X is 116 and now we know that Y plus Z must equal 116. And we can also get rid of the X here. Um, by plugging in 1 16.1 times 1 16 with a shave off 1.16 from 10. 36 that I will give points euro five y plus 0.1 z is equal to 9.2. Okay. And now from here we&#x27;re looking Teoh just to a matter of sip substitution to get rid of either wire Z and solved that way. So doing this with my plus C equals 1 16 Well, then, this gives that why must be equal to 1 16 minus c. Plugging that into the equation here gives 0.5 multiplied by 1 16 minus C plus 0.1 z is equal to 9.2. And solving this out we&#x27;ll get that Z is equal to 68. Z is equal to 68 hand. My policy must equal 1 16 Well, that 1 16 minus 68 is 48. So why must equal 48? So this tells us that Emily used 116 pennies, 48 nickels and 68.

Problem

Solve each problem by using a system of three equ…

Problem 52 Hard Difficulty

Answer

15,10,2

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