Question

A bag contains yellow marbles and red marbles, 80 in total. The number of yellow marbles is 2 more than 5 times the number of red marbles. How many yellow marbles are there?

Answer 1

In this problem, we're going to use variables and equations to represent the situation in the question.

• Let r represent the number of red marbles in the bag, and let y represent the number of yellow marbles in the bag.

The question says "The number of yellow marbles is 2 more than 5 times the number of red marbles." Using this information, we can create the equation:

`y=5r+2`

Also, we know there are 80 marbles total. We can also create the equation:

`r+y=80`

We're going to use the substitution method to solve this system of equations that we have created. Let's substitute
`y=5r+2` into the equation above so we can solve it:

`r+(5r+2)=80`

Remove parenthesis and combine like terms

`6r+2=80`

Subtract both sides by 2

`6r=78`

Divide both sides by 6.

`r=13`

There are 13 red marbles in the bag. However, we needed the amount of yellow marbles. The amount of yellow marbles is now easy to solve for since we have the number of red marbles.

Use the equation:
`r+y=80`

We know r is 13.

`13+y=80`

Subtract both sides by 13

`\boxed{y=67}`

There are 67 yellow marbles in the bag. Let me know if you need any clarifications, thanks!

~ Padoru