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) (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) (Show Source): You can put this solution on YOUR website!
p, Precy
a, Angelo
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-
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
in 3 years angelo will be 3x as old as his sister Precy:
(1)
a year ago angelo was 7 times as old as precy:
(2)
Set the two expressions for a equal to each other and solve for p:
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.
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