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QuestionA store sells a 2.5-pound bag of mixed nuts for \$9.25. Check if these bags are proportional: a. 4.4 lbs for \$16.28, b. 3.2 lbs for \$12. Yes/No.

Studdy Solution

STEP 1

Assumptions1. The weight of the mixed nuts is proportional to the price. This means that if we double the weight, the price should also double, and so forth. . The base price for comparison is a.5-pound bag of mixed nuts sold for $9.25.

STEP 2

First, we need to find the price per pound of the mixed nuts. We can do this by dividing the price of the bag by the weight of the bag.
Price per pound=Price of the bagWeight of the bagPrice\, per\, pound = \frac{Price\, of\, the\, bag}{Weight\, of\, the\, bag}

STEP 3

Now, plug in the given values for the price of the bag and the weight of the bag to calculate the price per pound.
Price per pound=$9.252.5 poundsPrice\, per\, pound = \frac{\$9.25}{2.5\, pounds}

STEP 4

Calculate the price per pound.
Price per pound=$9.252. pounds=$3.7 per poundPrice\, per\, pound = \frac{\$9.25}{2.\, pounds} = \$3.7\, per\, pound

STEP 5

Now that we have the price per pound, we can use this to determine if the other bags could have been sold by the grocery store. For each bag, we will multiply the weight by the price per pound and compare this to the actual price.
For bag aExpected price=Weight of the bag×Price per poundExpected\, price = Weight\, of\, the\, bag \times Price\, per\, poundExpected price=4.4 pounds×$3.7 per poundExpected\, price =4.4\, pounds \times \$3.7\, per\, pound

STEP 6

Calculate the expected price for bag a.
Expected price=4.4 pounds×$3. per pound=$16.28Expected\, price =4.4\, pounds \times \$3.\, per\, pound = \$16.28Since the expected price matches the actual price, bag a could have been sold by the grocery store. So, the answer for bag a is Yes.

STEP 7

Repeat the process for bag b.
Expected price=3.2 pounds×$3.7 per poundExpected\, price =3.2\, pounds \times \$3.7\, per\, pound

STEP 8

Calculate the expected price for bag b.
Expected price=3.2 pounds×$3.7 per pound=$11.84Expected\, price =3.2\, pounds \times \$3.7\, per\, pound = \$11.84Since the expected price does not match the actual price, bag b could not have been sold by the grocery store. So, the answer for bag b is No.
So, the final answers area. Yesb. No

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