Question

Gwen bought a total of 35 pieces of licorice. She bought 4 times as many red pieces as she did black pieces.

a. Write a system of equations that represents the number of pieces of each kind of licorice that Gwen bought.
b. Solve the system by substitution
c. Interpret the solution

Answer 1

Explanation:

The total no of pieces is 35. Let Gwen has B black pieces and R red pieces.

(a) She bought 4 times as many red pieces as she did black pieces. It means,

Red pieces = 4B

Equations that represents the number of pieces of each kind of licorice that Gwen bought are :

R + B = 35 ....(1)

and

R = 4B ....(2)

((b) Put equation (2) in equation (1)

4B + B = 35

5B = 35

B = 7

Put the value of B in equation (2)

R = 4(7) = 28

(c) There are 7 black and 28 red pieces of licorice.