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# Percentage/Algebra Question

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Given that x is 25% less than s and y is 20% great than x. Find y in terms of s.

Dec 14, 2015

#1
+24978
+15

Given that x is 25% less than s and y is 20% great than x. Find y in terms of s.

$$\begin{array}{rcl} y\cdot(100 \%+20\%) &=& x \\ x\cdot(100 \%-25\%) &=& s \\ \hline y\cdot(100 \%+20\%)\cdot(100 \%-25\%) &=& s \\ y\cdot( \frac{120}{100} )\cdot( \frac{75}{100} ) &=& s \\ y\cdot 1.2 \cdot 0.75 &=& s \\ y\cdot 0.9 &=& s \qquad & | \quad : 0.9\\ y &=& \frac{ s } {0.9} \\ y &=& \frac{ 10 } { 9 } s \\ y &=& 1.1\overline{1} s \\ \end{array}$$

Dec 14, 2015

#1
+24978
+15
$$\begin{array}{rcl} y\cdot(100 \%+20\%) &=& x \\ x\cdot(100 \%-25\%) &=& s \\ \hline y\cdot(100 \%+20\%)\cdot(100 \%-25\%) &=& s \\ y\cdot( \frac{120}{100} )\cdot( \frac{75}{100} ) &=& s \\ y\cdot 1.2 \cdot 0.75 &=& s \\ y\cdot 0.9 &=& s \qquad & | \quad : 0.9\\ y &=& \frac{ s } {0.9} \\ y &=& \frac{ 10 } { 9 } s \\ y &=& 1.1\overline{1} s \\ \end{array}$$