Question

Su has 5 times as many marbles as Bertha. When Su gives Bertha 10 marbles, they have the same amount. How many marbles did they EACH have at the begining? How many did they EACH have at the end?

Answer 1

Part A)

The number of marbles that Su has at the beginning is
`25`

The number of marbles that Bertha has at the beginning is
`5`

Part B)

The number of marbles that Su has at the end is
`15`

The number of marbles that Bertha has at the end is
`15`

Explanation:

Let

x------> number of marbles that Su has at the beginning

y------> number of marbles that Bertha has at the beginning

we know that

`x=5y` ----> equation A

`x-10=y+10` ----> equation B

substitute equation A in equation B

`(5y)-10=y+10`

`4y=20`

`y=5`

Find the value of x

`x=5(5)=25`

Part A) How many marbles did they EACH have at the begining?

The number of marbles that Su has at the beginning is
`25`

The number of marbles that Bertha has at the beginning is
`5`

Part B) How many did they EACH have at the end?

`x-10=y+10`

so

`25-10=5+10`

`15=15`

therefore

The number of marbles that Su has at the end is
`15`

The number of marbles that Bertha has at the end is
`15`