Question

Ms. Nina has 10 lbs of 25% sugar syrup. How much water does she need to add to make 10% sugar syrup?

Answer 1

She has 10lbs of 25% syrup... so, in the 10lbs, 25% of that is syrup, the rest, namely the 75% remaining is water or other substances.

let's say she adds "x" lbs of water, to get "y" lbs for the 10% mixture.

how much is 25% of 10lbs?  well, (25/100) * 10, or 2.5.

the water has no sugar syrup in it, so is just pure water, so the amoun of syrup in it is 0%, how much is 0% of "x" lbs?  well, (0/100) * x, or 0.00x, which is just 0.

how much is 10% of "y" lbs?  well (10/100) * y, or 0.10y.

whatever "x" and "y" are, we know that 10 + x = y.

we also know that the syrup amount in that is also 2.5 + 0.00x = 0.10y, thus


$\bf \begin{array}{lccclll} &\stackrel{lbs}{syrup}&\stackrel{concentration~\%}{syrup}&\stackrel{concentration}{amount}\\ &------&------&------\\ \textit{25\% syrup}&10&0.25&2.5\\ \textit{pur water}&x&0.00&0.00x\\ ------&------&------&------\\ \textit{10\% mixture}&y&0.10&0.10y \end{array} \\\\\\ \begin{cases} 10+x=\boxed{y}\\ 2.5+0.00x=0.10y\\ ----------\\ 2.5 = 0.10\left( \boxed{10+x} \right) \end{cases} \\\\\\ 2.5=1 + 0.10x\implies 1.5=0.10x \\\\\\ \cfrac{1.5}{0.10}=x\implies 15=x$

Answer 2

Answer:

The answer would be, 15

Step-by-step explanation:

25%*10lbs + 0%*x=10%(10+x)

250lbs+0lbs=100+10x

subtract 100 both sides and take out zero because it has no value

150=10x

divide ten both sides

150/10=15

so, x=15