. Shawn gets an allowance of $18 each week and his sister Natasha gets an allowance of $9 each week. Shawn saves 1/2 of his allowance, and Natasha saves 2/3 of her allowance. Suppose Shawn started with $0 savings, and Natasha started with $30. How many weeks will it take until they have the same amount in savings?

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berno berno · Answer 1 · 2021-03-22T05:51:14+01:00

Answer:

Shawn and Natasha have same amount in savings after [tex]10[/tex] weeks.

Step-by-step explanation:

Shawn gets an allowance of $18 each week.

Amount saved by Shawn = [tex]\frac{1}{2}(\$18)=\$9[/tex]

Natasha gets an allowance of $9 each week.

Amount saved by Natasha = [tex]\frac{2}{3}(\$9)=\$6[/tex]

Suppose that Shawn and Natasha have same amount in savings after [tex]x[/tex] weeks.

Also, Shawn started with $0 savings, and Natasha started with $30.

So,

[tex]9x=30+6x\\9x-6x=30\\3x=30\\x=10[/tex]

Therefore,

Shawn and Natasha have same amount in savings after [tex]10[/tex] weeks.