Question 1132373
let a equal the age of angelo totday.
let p equal the ager of precy today.


in 3 years angelo will be 3 times as old as precy.


equation for that is a + 3 = 3 * (p + 3).


a year ago angelo was 7 times as old as precy.


equation for that is a - 1 = 7 * (p - 1).


you have two equations that need to be solved simultaneously.


they are:


a + 3 = 3 * (p + 3)
a - 1 = 7 * (p - 1)


simplify both equations to get:


a + 3 = 3 * p + 9
a - 1 = 7 * p - 7


place the variables on the let side of the equal sign and the constants on the right side of the equal sign to get:


a - 3 * p = 9 - 3
a - 7 * p = -7 + 1


combine like terms in both equations to get:


a - 3 * p = 6
a - 7 * p = -6


subtract the second equation from the first to get:


4 * p = 12


solve for p to get p = 12 / 4 = 3


that's precy's age today.


replace p with 3 in either of the original equations as shown below.


the two original equations are:


a + 3 = 3 * (p + 3)
a - 1 = 7 * (p - 1)


the first equation becomes a + 3 = 3 * 6 which a + 3 = 18 which becomes a = 15.


the second equation becomes a - 1 = 7 * 2 which becomes a - 1 = 14 which becomes a = 15.


that's the age of angelo today.


you have:


a = 15
p = 3


in 3 years, a = 18 and p = 6 which makes a = 3 times p.


one year ago, a was 14 and p was 2 which made a = 7 times p.


solution looks good.


solution is:


angelo is 15 years old and precy is 3.