Question

How much water do you add  to make 12% sugar syrup using 5g sugar?

Answer 1

`36(2)/(3)` g of water.

Explanation:

You know that 5 g of sugar form 12%. Let x g be the amount of water needed. The total amount of syrup will be x+5 g. Then

5 g - 12%,

x+5 g - 100%.

Mathematically, you can write a proportion:

`(5)/(x+5)=(12)/(100)\Rightarrow 500=12(x+5),\ 500=12x+60,\ 12x=440, \\ \\x=(440)/(12)=(110)/(3)=36(2)/(3).`

Answer 2

so the syrup is just water and sugar, we know that the sugar percent is just 12%, and that happens to be 5grams.

now 100% - 12% is 88%, so the 88% leftover will just be water.

if 12% is 5g, how much is 88%?

`\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 5&12\\ x&88 \end{array}\implies \cfrac{5}{x}=\cfrac{12}{88}\implies \cfrac{5}{x}=\cfrac{3}{22}\implies 110=3x \\\\\\ \cfrac{110}{3}=x\implies 36(2)/(3)=x`