



 
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
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 \[4a + 12b 12 b = 42b  12 b\] so \[4a = 30b.\] Finally multiplying each side by $\large \frac{1}{4b}$ gives \[\frac{1}{4b} \times 4a = \frac{1}{4b} \times 30b.\] or \[\frac{a}{b} = \frac{30}{4} = \frac{15}{2}.\] Penny
 


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