How many ounces does each package of candy weight ?

Question

A candy company packages chocolate gift boxes using white chocolate , milk chocolate and dark chocolate. A box of 1 package of white chocolate , 3 packages of milk chocolate, and 3 packages of dark chocolate weights 14 ounces.

A box of 1 package of white chocolate , 3 packages of milk chocolate, and 4 packages of dark chocolate weights 17 ounces.

A box of 1 package of white chocolate , 4 packages of milk chocolate, and 3 packages of dark chocolate weights 15 ounces.

Answer 1

This is a systems of equations problem. You have three variables:

Let W = weight of white chocolate package

Let M = weight of milk chocolate package

Let D = weight of dark chocolate package

Now create your three equations:

(A) 1W + 3M + 3D = 14

(B) 1W + 3M + 4D = 17

(C) 1W + 4M + 3D = 15

You do not even need to do all the algebra to figure out these equations. Look at equation A vs equation B. The only difference is an additional package of dark chocolate. The weight went from 14 to 17... so the difference in weight is 3 ounces. Therefore one package of dark chocolate weighs 3 ounces.

Likewise, look at the difference between equation A and equation C. The only difference is one added package of MILK chocolate. The weight has increased by 1 ounces for this additional package. Therefore one package of milk chocolate weighs 1 ounce.

Use the values for M = 2 and D = 3 to figure out the value for the white chocolate package, using any of the equations. If you use equation A, you will substitute and find:

(A) 1W + 3M + 3D = 14

W + 3(1) + 3(3) = 14

W + 3 + 9 = 14

W = 14 - 12

W = 2

Now plug these into B and C to check your answer! Always check your answer... it will save your grade.