Question

Joachim has 2/3 as many marbles as Leanne. Leanne has 1/2 as many marbles as Alex. If Alex has 36 more than Joachim, how many marbles do they have altogether?

Answer 1

99 marbles

Explanation:

Let number of marbles with Alex be
`x`

Leanne has 1/2 as many marbles as Alex.

So,

Number of marbles with Leanne =
`(x)/(2)`

Number of marbles with Joachim =
`(2)/(3)((x)/(2))=(x)/(3)`

Also, Alex has 36 more marbles than Joachim.

So,

Number of marbles with Alex = 36 + Number of marbles with Joachim

=
`36+(x)/(3)`

So,

`x=36+(x)/(3)\\\\x-(x)/(3)=36\\\\(2x)/(3)=36\\\\\x=36((3)/(2))\\\\x=54`

So,

Number of marbles with Alex = 54

Number of marbles with Leanne =
`(x)/(2)=(54)/(2)=27`

Number of marbles with Joachim =
`(x)/(3)=(54)/(3)=18`

Total number of marbles =
`54+27+18=99`