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Interpreting Situations as Functions

A lawn mowing service charges a $10 flat rate, plus$ 7 per hour. Write an equation for the cost of a job as a function of the hours it takes. If a particular lawn costs $38 to mow, how many hours did it take?

$cost=c$
$hours=h$

$h=0,\ c=10,\ (0,\ 10)$

$h=1,\ c=17,\ (1,\ 17)$

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{17-10}{1-0}=7$

$b=10,\ (0,\ 10)$

$y=mx+b\rightarrow y=7x+b\rightarrow y=7x+10\rightarrow c=7h+10$

$38=7h+10\rightarrow 38-10=7h+10-10\rightarrow \frac{28}{7}=\frac{7h}{7}\rightarrow 4=h$

One number is twice as large as three more than another number. The product of the numbers is 20. What are they?

$x=2(y+3)$
$(x)(y)=20$

Substitute eq 1. into eq 2.

$[2(y+3)](y)=20$

$(2y+6)(y)=20$

$\frac{2y^{2}}{2}+\frac{6y}{2}=\frac{20}{2}$

$y^{2}+3y=10$

$y^{2}+3y-10=0$

$factors\ of\ -10:\ [\pm 1,\ \pm 10],\ [\pm 5,\ \pm 2]$

$(y+5)(y-2)=0$

$y+5=0\rightarrow y=-5$

$y-2=0\rightarrow y=2$

Substitute back into eq 2.

$(x)(-5)=20\rightarrow \frac{(x)(-5)}{-5}=\frac{20}{-5}\rightarrow x=4$

$(x)(2)=20\rightarrow \frac{(x)(2)}{2}=\frac{20}{2}\rightarrow x=10$

Two solutions:

$x=-4,\ y=-5$
$x=10,\ y=2$