Question

A bag contains purple marbles and red marbles, 34 in total. The number of purple marbles is 8 less than 5 times the number of red marbles. How many purple marbles are there?

Answer 1

27 purple marbles

Explanation:

Let p = purple marbles

r= red marbles

p = 5r-8

p+r = 34

Replace p in the second equation with 5r-8 from the first equation

p+r = 34

5r-8 +r = 34

Combine like terms

6r -8 = 34

Add 8 to each side

6r-8+8 = 34+8

6r = 42

Divide each side by 6

6r/6 = 42/6

r= 7

We want to find p

p+r = 34

p+7 = 34

Subtract 7 from each side

p+7-7 = 34-7

p =27