Ahmed burns $8$ calories every $2$ minutes when doing push-ups and he burns $10$ calories every $2$ minutes when jumping rope. If Ahmed wants to burn $150$ calories in total, which of the following equations could represent the relationship between $p$ , the number of minutes Ahmed does push-ups, and $j$ , the number of minutes that Ahmed jumps rope? $\newline$ Choose $1$ answer: $\newline$ (A) $4 p+5 j=150$ $\newline$ (B) $\frac{p}{4}+\frac{j}{5}=\frac{1}{150}$ $\newline$ (C) $\frac{150}{4} p+\frac{150}{5} j=150$ $\newline$ (D) $\frac{4}{150} p+\frac{5}{150} j=\frac{1}{150}$

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Grade 8

Evaluate a linear function: word problems

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Q. Ahmed burns

8

calories every

2

minutes when doing push-ups and he burns

10

calories every

2

minutes when jumping rope. If Ahmed wants to burn

150

calories in total, which of the following equations could represent the relationship between

p

, the number of minutes Ahmed does push-ups, and

j

, the number of minutes that Ahmed jumps rope?

\newline

Choose

1

answer:

\newline

(A)

4 p+5 j=150

\newline

(B)

\frac{p}{4}+\frac{j}{5}=\frac{1}{150}

\newline

(C)

\frac{150}{4} p+\frac{150}{5} j=150

\newline

(D)

\frac{4}{150} p+\frac{5}{150} j=\frac{1}{150}

Establishing calorie burn rates: First, we need to establish the rate at which Ahmed burns calories for each activity. For push-ups, he burns $8$ calories every $2$ minutes, which is equivalent to $4$ calories per minute. This means that for every minute Ahmed does push-ups, he burns $4$ calories.
Calculating total calories burned: Similarly, for jumping rope, Ahmed burns $10$ calories every $2$ minutes, which is equivalent to $5$ calories per minute. So, for every minute Ahmed jumps rope, he burns $5$ calories.
Checking the equation options: Now, we need to find an equation that relates the total calories burned $150$ to the number of minutes spent doing push-ups $p$ and the number of minutes spent jumping rope $j$ . The total calories burned from push-ups would be $4$ calories/minute times the number of minutes $p$ , and the total calories burned from jumping rope would be $5$ calories/minute times the number of minutes $j$ .
Selecting the correct equation: The equation that represents the total calories burned from both activities is the sum of the calories burned from push-ups and the calories burned from jumping rope, which should equal $150$ calories. So, the equation is $4p + 5j = 150$ .
Selecting the correct equation: The equation that represents the total calories burned from both activities is the sum of the calories burned from push-ups and the calories burned from jumping rope, which should equal $150$ calories. So, the equation is $4p + 5j = 150$ . Now, let's check the given options to see which one matches our equation. Option (A) is $4p + 5j = 150$ , which is exactly what we derived.
Selecting the correct equation: The equation that represents the total calories burned from both activities is the sum of the calories burned from push-ups and the calories burned from jumping rope, which should equal $150$ calories. So, the equation is $4p + 5j = 150$ . Now, let's check the given options to see which one matches our equation. Option (A) is $4p + 5j = 150$ , which is exactly what we derived. Option (B) is $\frac{p}{4} + \frac{j}{5} = \frac{1}{150}$ , which does not match our equation because it suggests that the sum of the fractions of minutes spent on each activity equals $\frac{1}{150}$ , which is not correct in terms of the calories burned.
Selecting the correct equation: The equation that represents the total calories burned from both activities is the sum of the calories burned from push-ups and the calories burned from jumping rope, which should equal $150$ calories. So, the equation is $4p + 5j = 150$ . Now, let's check the given options to see which one matches our equation. Option (A) is $4p + 5j = 150$ , which is exactly what we derived. Option (B) is $\frac{p}{4} + \frac{j}{5} = \frac{1}{150}$ , which does not match our equation because it suggests that the sum of the fractions of minutes spent on each activity equals $\frac{1}{150}$ , which is not correct in terms of the calories burned. Option (C) is $\frac{150}{4}p + \frac{150}{5}j = 150$ , which is incorrect because it multiplies the number of minutes by the fraction of the total calories, which does not represent the rate of calories burned per minute.
Selecting the correct equation: The equation that represents the total calories burned from both activities is the sum of the calories burned from push-ups and the calories burned from jumping rope, which should equal $150$ calories. So, the equation is $4p + 5j = 150$ . Now, let's check the given options to see which one matches our equation. Option (A) is $4p + 5j = 150$ , which is exactly what we derived. Option (B) is $\frac{p}{4} + \frac{j}{5} = \frac{1}{150}$ , which does not match our equation because it suggests that the sum of the fractions of minutes spent on each activity equals $\frac{1}{150}$ , which is not correct in terms of the calories burned. Option (C) is $\frac{150}{4}p + \frac{150}{5}j = 150$ , which is incorrect because it multiplies the number of minutes by the fraction of the total calories, which does not represent the rate of calories burned per minute. Option (D) is $\frac{4}{150}p + \frac{5}{150}j = \frac{1}{150}$ , which is incorrect because it divides the rate of calories burned per minute by the total calories, which does not make sense in the context of the problem.
Selecting the correct equation: The equation that represents the total calories burned from both activities is the sum of the calories burned from push-ups and the calories burned from jumping rope, which should equal $150$ calories. So, the equation is $4p + 5j = 150$ . Now, let's check the given options to see which one matches our equation. Option (A) is $4p + 5j = 150$ , which is exactly what we derived. Option (B) is $\frac{p}{4} + \frac{j}{5} = \frac{1}{150}$ , which does not match our equation because it suggests that the sum of the fractions of minutes spent on each activity equals $\frac{1}{150}$ , which is not correct in terms of the calories burned. Option (C) is $\frac{150}{4}p + \frac{150}{5}j = 150$ , which is incorrect because it multiplies the number of minutes by the fraction of the total calories, which does not represent the rate of calories burned per minute. Option (D) is $\frac{4}{150}p + \frac{5}{150}j = \frac{1}{150}$ , which is incorrect because it divides the rate of calories burned per minute by the total calories, which does not make sense in the context of the problem. Therefore, the correct equation that represents the relationship between the number of minutes Ahmed does push-ups ( $p$ ) and the number of minutes Ahmed jumps rope ( $j$ ) to burn $150$ calories is given by option (A), which is $4p + 5j = 150$ .