The wage of jack is increased by 15% and at the same time, the working hours is decreased by 10%. Then, by what percent the hourly wage of jack is decreased or increased? (approximately)
I tried $\frac{\frac{1.15w}{.9h}-\frac{w}{h}}{\frac{w}{h}}$. Where am I going wrong? The answer is increase of 28%. Please explain.
I'm assuming Wage = Hourly Wage $\times$ Hours
You could say $$W=hw\times h\\W+15\%=hw\times (h-10\%)\\1.15=hw\times .90\\hw=1.28$$
This is saying the Wage went up by 0.15, the hours went down by 0.10 and the hourly wage went up by 0.28
EDIT: I bet this makes more sense. $$hw_{old}=\frac{W}{h}\\hw_{new}=\frac{1.15W}{0.9h}\\\frac{hw_{new}}{hw_{old}}=\frac{\frac{1.15W}{0.9h}}{\frac{W}{h}}=1.28$$
Maybe where you went wrong was subtracting out the $\frac{W}{h}$ in the middle of the expression instead of subtracting $1$ from $1.28$?