Choose a variable, write an equation for each problem and then solve

1. If a number is 11 more than 6 what is the number
2. If 3 less than a number is 10 what is the number
3. If 14 more than a number is 12 what is the number
4. If a number is 5 less than 23 what is the number
5. If a number plus 4 equals two times 6 what is the number
6. If a number minus 10 equals four times 15 what is the number

the answer is a

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