Question

A bag contains half as many

yellow marbles as purple marbles. There
are 36 marbles in the bag. Write and solve a
system of equations to find the number of
marbles of each color.

Answer 1

There are 24 purple marbles and 12 yellow marbles

Solution:

Let "y" be the number of yellow marbles

Let "p" be the number of purple marbles

Given that, a bag contains half as many yellow marbles as purple marbles

Therefore, number of yellow marbles = half of number of purple marbles

y = half of p

`y = (p)/(2)`

2y = p ---- eqn 1

There are 36 marbles in the bag

number of yellow marbles + number of purple marbles = 36

y + p = 36 ---- eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 1 in eqn 2

y + 2y = 36

3y = 36

y = 12

Substitute y = 12 in eqn 2

12 + p = 36

p = 36 - 12

p = 24

Thus there are 24 purple marbles and 12 yellow marbles