Question

Question 19
A game consists of black and white pieces. The number of black pieces is 5 more than 3 times the white pieces. Seven white and 15 black pieces are removed each round. After several rounds, there are 3 white and 56 black pieces left. How many pieces were there in the beginning?
A. 52
B. 158
C. 210
D. 213
E. 218

Answer 1

Answer:

• D. 213

Step-by-step explanation:

The number of black pieces is 5 more than 3 times the white pieces:

• b = 3w + 5

Let the number of rounds is x.

Initial number of white nd black pieces:

• w = 7x + 3
• b = 15x + 56

Substitute the values of b and w into first equation and find the value of x:

• 15x + 56 = 3(7x + 3) + 5
• 15x + 56 = 21x + 14
• 6x = 42
• x = 7

Find the number of pieces:

• w = 7*7 + 3 = 52
• b = 3*52 + 5 = 161
• w + b = 52 + 161 = 213

Correct choice is D

Answer 2

Answer:

A game consists of black and white pieces. The number of black pieces is 5 more than 3 times the white pieces. Seven white and 15 black pieces are removed each round. After several rounds, there are 3 white and 56 black pieces left. How many pieces were there in the beginning?

A. 52

B. 158

C. 210

D. 213

E. 218