Maths Olympiad Prep

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Algebra Difficulty 1.8 Junior Find the answer

What is the value of mm if Tobias downloads mm apps, each app costs $2.00\$ 2.00 plus 10%10 \% tax, and he spends $52.80\$ 52.80 in total on these mm apps?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Since the tax rate is 10%10 \%, then the tax on each $2.00\$ 2.00 app is $2.00×10100=$0.20\$ 2.00 \times \frac{10}{100}=\$ 0.20.
Therefore, including tax, each app costs $2.00+$0.20=$2.20\$ 2.00+\$ 0.20=\$ 2.20.
Since Tobias spends $52.80\$ 52.80 on apps, he downloads $52.80$2.20=24\frac{\$ 52.80}{\$ 2.20}=24 apps.
Therefore, m=24m=24.

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