Question

Bob ate 10 carrots and 7 Hershey’s kisses and the total calories were 263. Fred ate 4 carrots and 8 Hershey’s kisses and the total calories were 230. How many calories are in a carrot and a Hershey’s kiss?

Answer 1

There are 9.5 calories in the carrot and 24 calories in the Hershey’s kiss

Explanations:

Let the amount of calories in a carrot be "x"

Let the amount of calories in Hershey's kiss be "y"

If Bob ate 10 carrots and 7 Hershey’s kisses and the total calories were 263, then;

10x + 7y = 263 .............................. 1

Similarly if Fred ate 4 carrots and 8 Hershey’s kisses and the total calories were 230, then;

4x + 8y = 230

2x + 4y = 115 ................................2

Solve equation 1 and 2 simultaneously

10x + 7y = 263 .............................. 1 * 1

2x + 4y = 115 ................................2 * 5

_______________________________

10x + 7y = 263

10x + 20y = 575

Subtract

7y - 20y =263 - 575

-13y = -312

y = 312/13

y = 24

Substitute y = 24 into equation 2 to determine "x"

2x + 4y = 115

2x + 4(24) = 115

2x + 96 =115

2x = 115 - 96

2x = 19

x = 19/2

x = 9.5

Hence there are 9.5 calories in the carrot and 24 calories in the Hershey’s kiss