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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?

Sagot :

Answer:

99 marbles

Step-by-step explanation:

Let number of marbles with Alex be [tex]x[/tex]

Leanne has 1/2 as many marbles as Alex.

So,

Number of marbles with Leanne = [tex]\frac{x}{2}[/tex]

Number of marbles with Joachim = [tex]\frac{2}{3}(\frac{x}{2})=\frac{x}{3}[/tex]

Also, Alex has 36 more marbles than Joachim.

So,

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

= [tex]36+\frac{x}{3}[/tex]

So,

[tex]x=36+\frac{x}{3}\\\\x-\frac{x}{3}=36\\\\\frac{2x}{3}=36\\\\\x=36(\frac{3}{2})\\\\x=54[/tex]

So,

Number of marbles with Alex = 54

Number of marbles with Leanne = [tex]\frac{x}{2}=\frac{54}{2}=27[/tex]

Number of marbles with Joachim = [tex]\frac{x}{3}=\frac{54}{3}=18[/tex]

Total number of marbles = [tex]54+27+18=99[/tex]

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