Question

A bag of marbles contains only yellow and purple marbles. The number of yellow marbles is five times as the purple marbles. The bag contains 138 total marbles. develop a system of equations to represent the situation, determine how many of each color of marble is in the bag

show how you checked your answers ​

Answer 1

23 purple marbles

115 yellow marbles

Explanation:

Let y represent the yellow marble

Let p represent the purple marbles

So, we have the equations

y = 5p

Therefore, y + p = 138

5p + p = 138

6p = 138

p = 23 marbles

Now let's put 23 in for the p in the equation to find the number of yellow marbles

y = 5(23)

y = 115 marbles

Answer 2

First create a system of equations:
y = number of yellow marbles
p = number of purple marbles
y = 5p
y + p = 138
Now since we already have one of the variables (y) by itself in the first equation, we can substitute that into the second equation so we only have one variable (p) and it’s easier to solve.
(5p) + p = 138
Combine like terms
6p = 138
Divide both sides by 6
p = 23
Now that we have p, we can substitute it in the first equation so we only have one variable (y) and it’s easier to solve.
y = 5(23)
y = 115
So there’s are 23 purple marbles and 116 yellow marbles.
To check our answers, add together the purple and yellow marble numbers that we got to see if it equals 138 to see if they fit into the equations.
23 + 115 = 138
138 = 138
Also, we can check if there are 5 times as many yellow marbles as purple marbles.
115 = 5 x 23
115 = 115
Since we got a valid equation, the answers are correct.