How many hours did she work?

Last week, Lindsay earned $10 per hour plus a $60 bonus for good job performance. 
She spends 1/15 of her paycheck on dinner with friends. If she had not earned the bonus, the amount
she spent on dinner would have been 1/10 of her paycheck. Which equation can be used to find h,
​the number of hours Lindsay worked last week?

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You don’t know how much she spent on dinner, nor the number of hours she worked.
Let variables represent those two things.

y = total amount she spent on dinner
h = number of hours

Set up a system of equations to model the two situations, one with bonus and one without bonus.

y = (1/15)(10h + 60) {amount spent with bonus}
y = (1/10)(10h) {amount spent without bonus}

y = (2/3)h + 4   {used distributive property in first equation}
y = h {multiplied 1/10 by 10 in second equation}

Solve the system of equations for h, by substituting h, in for y, into first equation.

h = (2/3)h + 4   {substituted h, in for y, into first equation}
(1/3)h = 4 {subtracted (2/3)h from each side}
h = 12  {multiplied each side by 3}

She worked 12 hours.

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