SOLUTION: in 3 years angelo will be 3x as old as his sister Precy, a year ago angelo was 7 times as old as precy how old are they now

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Question 1132373: in 3 years angelo will be 3x as old as his sister Precy, a year ago angelo was 7 times as old as precy how old are they now
Found 3 solutions by Theo, josgarithmetic, greenestamps:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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.


Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
p, Precy
a, Angelo

system%28a%2B3=3%28p%2B3%29%2Ca-1=7%28p-1%29%29

-

system%28a%2B3=3p%2B9%2Ca-1=7p-7%29

system%28a-3p=6%2Ca-7p=-6%29

E1-E2
4p=12
highlight%28p=3%29
-
highlight%28a=15%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


in 3 years angelo will be 3x as old as his sister Precy:

a%2B3+=+3%28p%2B3%29
a%2B3+=+3p%2B9
a+=+3p%2B6 (1)

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

a-1+=+7%28p-1%29
a-1+=+7p-7
a+=+7p-6 (2)

Set the two expressions for a equal to each other and solve for p:

3p%2B6+=+7p-6
12+=+4p
p+=+3

Precy is 3 years old; 1 year ago he was 2. 1 year ago Angelo was 7 times as old as precy, so he was 14 1 year ago; so he is now 15.

ANSWERS: Precy is 3; Angelo is 15.

If this were a problem on a math competition test where the speed of solving is important, the problem can be solved much faster by logical trial and error.

(1) Choose an age for Precy 1 year ago and make Angelo's age 7 times that number;
(2) Add 4 years to each of those ages to get their ages 3 years from now and see if those ages have Angelo 3 times as old a Precy.

Precy 1 year ago = 1; Angelo 1 year ago = 7; Precy 3 years from now 5, Angelo 3 years from now 11. No; 11 is not 3 times 5.

Precy 1 year ago = 2; Angelo 1 year ago = 14; Precy 3 years from now 6, Angelo3 years from now 18. YES! 18 is 3 times 6. Their ages 1 year ago were 2 and 14; their ages now are 3 and 15.

That solution takes a long time to write out; but the mental calculations are quick and easy.