Question

ella is cooking a turkey and a ham. it takes 15 minutes per pound to cook a turkey and 23 minutes per pound to cook a ham. ella is able to cook the turkey and the ham in 4 hours and 25 minutes. if the turkey weighs twice as much as the ham, how much do the turkey and the ham weigh?
a. the turkey weighs 10 pounds, and the ham weighs 5 pounds.
b. the turkey weighs 5 pounds, and the ham weighs 5 pounds.
c. the turkey weighs 20 pounds, and the ham weighs 10 pounds.
d. the turkey weighs 5 pounds, and the ham weighs 10 pounds.

Explanation:

Step1: Convert total time to minutes

4 hours = \(4\times60 = 240\) minutes, total time = \(240 + 25 = 265\) minutes? Wait, no, wait. Wait, the problem says "4 hours and 25 minutes" – wait, no, let's re - read. Wait, the cooking time: turkey is 15 minutes per pound, ham is 23 minutes per pound? Wait, no, wait the original problem: "It takes 15 minutes per pound to cook a turkey and 23 minutes per pound to cook a ham. Ella is able to cook the turkey and the ham in 4 hours and 25 minutes." Wait, 4 hours is 240 minutes, 240 + 25 = 265 minutes? Wait, no, maybe I misread. Wait, no, let's check the options. Wait, maybe the total time is 4 hours and 25 minutes? Wait, no, let's define variables. Let \(h\) be the weight of ham in pounds, then turkey weight \(t = 2h\) (since turkey weighs twice as much as ham). Cooking time for turkey: \(15t\) minutes, cooking time for ham: \(23h\) minutes. Total time: \(15t+23h = 4\times60 + 25=240 + 25 = 265\) minutes? Wait, but let's substitute \(t = 2h\) into the equation: \(15\times(2h)+23h=30h + 23h = 53h\). Then \(53h=265\), so \(h = 265\div53 = 5\) pounds. Then \(t = 2\times5 = 10\) pounds? Wait, but that doesn't match the options. Wait, maybe I made a mistake in the cooking time per pound. Wait, maybe the turkey is 15 minutes per pound, ham is 23? No, wait the options: let's check option D: turkey 5 pounds, ham 10? No. Wait, option C: turkey 20, ham 10. Wait, maybe I misread the cooking time. Wait, maybe the turkey is 15 minutes per pound, ham is 23? No, wait the problem says "15 minutes per pound to cook a turkey and 23 minutes per pound to cook a ham" – no, maybe it's 15 for turkey and 25? Wait, no, the total time is 4 hours and 25 minutes. Wait, 4 hours is 240, 240 + 25 = 265. Wait, let's try option D: turkey 5, ham 10. Then turkey time: \(15\times5 = 75\), ham time: \(23\times10 = 230\), total \(75 + 230 = 305\), too much. Option C: turkey 20, ham 10. Turkey time: \(15\times20 = 300\), ham time: \(23\times10 = 230\), total 530, too much. Option B: turkey 5, ham 5. Turkey time: \(15\times5 = 75\), ham time: \(23\times5 = 115\), total 190, no. Option A: turkey 10, ham 5. Turkey time: \(15\times10 = 150\), ham time: \(23\times5 = 115\), total 265. Ah! There we go. So \(t = 10\), \(h = 5\), which is option A. Wait, let's redo the steps correctly.

Step1: Define variables

Let \(h\) = weight of ham (in pounds), \(t\) = weight of turkey (in pounds). Given \(t = 2h\) (turkey weighs twice as much as ham).

Step2: Calculate total cooking time in minutes

4 hours and 25 minutes = \(4\times60+25=240 + 25 = 265\) minutes.

Step3: Set up the cooking time equation

Cooking time for turkey: \(15t\) minutes (15 minutes per pound), cooking time for ham: \(23h\) minutes (23 minutes per pound). So total time: \(15t + 23h=265\).

Step4: Substitute \(t = 2h\) into the equation

Substitute \(t = 2h\) into \(15t + 23h\):
\(15\times(2h)+23h=30h + 23h = 53h\)

Step5: Solve for \(h\)

We have \(53h = 265\), so \(h=\frac{265}{53}=5\) pounds.

Step6: Solve for \(t\)

Since \(t = 2h\), \(t = 2\times5 = 10\) pounds.

Answer:

A. The turkey weighs 10 pounds, and the ham weighs 5 pounds.