word problem?

Question

How would you solve this problem using 2 equations with 2 variables?

Loren's marble jar contains plain marbles and colored marbles. If there are 32 more plain marbles than colored marbles and there are 180 marbles in the jar, how many colored marbles does Lauren have?

Answer 1

Let x represent the plain marbles.
Let y represent the colored marbles.

We have 32 more plain marbles than colored marbles, so this means that x+32=y OR x-y=-32

We have 180 marbles in total, so that means x+y=180

We thus have 2 equations
x-y=-32
x+y=180

Add the 2 equations together (y cancels out), so we get
2x = 212
x= 106

Since we have 180 total marbles in the jar,
180-106=74=y

So we have 106 plain marbles, and 74 colored marbles.
[Answer: 106 plain marbles, and 74 colored marbles]

Answer 2

Let p = # of plain marbles.
Let c = # of colored marbles.
These are your two variables.

Equation 1: There are 32 more plain marbles than colored marbles
p = c + 32

Equation 2: There are 180 marbles in the jar
c + p = 180

Method to solve: Substitution
Take equation 1 and plug it into equation 2:
c + (c + 32) = 180
Simplify by combining the c's and moving the 32 to the other side:
2c = 180 - 32
2c = 148
Divide by 2 on both sides to get p:
c = 74

So, Lauren has 74 colored marbles and 106 plain marbles.

Answer 3

c + c + 32 = 180 => 2c = 148 => c = 74
74 coloured, 106 white = total 180