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Pranav bought exactly 220 pounds of candy in small boxes that hold exactly 7 pounds of candy and large boxes that hold exactly 32 pounds of candy. How many small boxes did Pranav buy?

 

I need halp! ASAP!

 Jun 16, 2021
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Let x be the number of small boxes and y be the number of large boxes. Both x and y must be whole numbers. The total mass of candy must be 220 pounds.

 

7x + 32y = 220

 

Find the expression of x in terms of y.

 

7x = 220 - 32y

\(x = {220 - 32y \over 7}\frac{}{}\)     
 

The value of x can be solved using trial and error. The value of x must be a whole number. Start from the largest value of y that is possible by equating x to 0.

 

7(0) + 32y = 220

\(y = {220 \over 32}\frac{}{}=6.875 \rightarrow y = 6\)
 

The largest value of y is 6. Start the trial and error from y = 6,5,4....

 

   y = 6 -> x = 220 - 32(6)/7 = 28/7 = 4 (Whole Number!)

 

From the first guess, the number of large boxes is 6 and the number of small boxes is 4.

 

The number of small boxes is 4.

 Jun 21, 2021

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