Math CentralQuandaries & Queries


Question from Jenny, a teacher:

If a + 3b is equal to $175\%$ of 6b, what is the value of a/b?

Hi Jenny,

$175\% = \large \frac{175}{100} = \frac{7}{4}$ so "a + 3b is equal to $175\%$ of 6b" can be written

\[a + 3b = \frac74\times 6b\]

Manipulate this equation until it is in the form

\[\mbox{ (a number) } \times a = \mbox{ (a number) } \times b\]

from which yo can find the value of $\large \frac{a}{b}.$

I hope this helps. Write back if you need more assistance,

Jenny wrote back

Thanks Penny for helping me with this problem. It is a question from a middle school math competition. The final answer is 15/2 and I did the exact same work you did, but cannot seem to get that solution.

Hi Jenny,

I multiplied both sides of the equation

\[a + 3b = \frac74\times 6b\]

by 4 to clear the fraction and got

\[4a + 12b = 7 \times 6b = 42b.\]

Adding $-12 b$ to each side gives

\[4a + 12b -12 b = 42b - 12 b\]


\[4a = 30b.\]

Finally multiplying each side by $\large \frac{1}{4b}$ gives

\[\frac{1}{4b} \times 4a = \frac{1}{4b} \times 30b.\]


\[\frac{a}{b} = \frac{30}{4} = \frac{15}{2}.\]



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