If AB = 13x - 29 and AC = 6x + 17 and BC = 5x + 3, FIND x

Step-by-step explanation:

Just translate the words to numbers. Twice the number of dimes is 2d . Five less means subtract 5 from that. thats the nunber of nickels: n

So your first equation is n = 2d- 5

you know that the value of a nickel is 5 and the value of a dime is 10 and the total value is 115. (skip the decimals for now!) It's all cents. (that should make sense!)

The second equation is 5n + 10d = 115

Substitute the value of n (2d-5) from the first equation into the place of n in the second equation.

5(2d -5) + 10d = 115    now Distribute

10d -25 + 10d =115  and solve for d (add 25 to both sides abd combine d's)

10d + 10d = 115 + 25

20d = 140  divide both sides by 20

d = 7  Put that value in place of d in the first equation and solve for n

n= 2(7) -5  That's 14-5 so    n=9

Check values in either equation: 5n + 10d= 115

5(9) + 10(7) = 115  

45 + 70 = 115  TRUE! so  Jon has  9 nickels and 10 dimes.