Jackie had 2 part time jobs at Shoney's Restaurant. One week she earned a total of $306, working 12 hours as a cashier and 10 hours as a cook. The next week, she
worked 14 hours as a cashier and 22 hours as a cook, earning $512. How much does
she earn per hour as a cashier?

x = 12

y = 15

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4