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Last week, Emily paid $\$ 8.25$ for $x$ pounds of apples. This week she paid $\$ 9.50$ for $(x+1)$ pounds of apples. The price per pound was the same each week. How many pounds of apples did Emily buy each week and what was the price per pound? (Use $\frac{\text { total cost }}{\text { number of pounds }}=$ cost per pound for each week.)

Last week 6.6 pounds, this week 7.6 pounds, $\$ 1.25$ per pound

Algebra

Chapter 2

THE RATIONAL NUMBERS

Section 7

Solving Rational Equations

Fractions and Mixed Numbers

Decimals

Equations and Inequalities

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Okay, guys. So in this prove problem, we're gonna work. Problem. And it says that last week Emily bought X pounds of apples. She bought X pounds of apples for $8.25 and it says that this week she brought X plus one pounds of apples for $9.50. And it says that throughout each week, the price per pound basically the rate the price per pound of the apples was uniform didn't change from week to week. And the question is says, how many pounds of apples did she buy per week? And part B is. What was the price per pound? So first? Well, the part of the problem that's really important to us is this fact right here. The fact that the price per pound was the same, it allows us to set an equality function up and it a lot. It'll allow us to solve for the value of X. So what is price per pound? Price per pound is the same thing has cost over total wheat over total weight. So, given that information, let's take a look at the, uh, price per pound. Last week, the first week that she bought the apples. That's gonna be ex. That's not the ex. Im sorry. That's gonna be eight point 25 divided by X and that's gonna be equal to the price per pound of the week the current week because the price per pound his uniform. So that's gonna be 9.5 over X plus one. Now we can cross multiply. Basically, cross multiplying is multiplying this way, this way and that keeps the inequality the same. So that's gonna give us 8.25 x plus 8.25 I just distributed in the process, too. And that's gonna be equal to 9.50 X. We're going to subtract 8.25 acts on both sides, and that's gonna give us 1.25 x. And when you divide by 1.25 on both sides, that's going to give us 6.6. And now that's gonna be the pounds that she bought last week. So our value of X is 6.6. So for part a last week, I'll just do has last week she bought 6.6 pounds and I'll say T w for this week, and this week she bought X plus one pounds. So 6.6 plus one at 7.6 pounds. And now our second part of the problem says, find out the price per pound rifle probably said was cost over pounds. Now we have a numerical value for, um, pounds. So let's do 8.25 over 6.6 evaluated. This gives us 1.25 This gives us $1.25 per pound just if you put the units. So our answer to part B. Uh, dollar 25 her pound. I hope this help guys, um, with hope helps all this work problem, but it was understandable.

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