Question 114144: please help me with this problem, i try to solve it by studying your examples, but i really can't get it right...here's the problem:
PERLA IS NOW 5 TIMES AS OLD AS MARILOU. IN 10 YEARS, PERLA WILL BE 3 TIMES AS OLD AS MARILOU. HOW OLD IS EACH? Kindly solve and show the solution. Below is my attempt to solve it. But I guess, its wrong.
Here's my attempt:
let P be Perla's age and M be Marilou's age
a) P = 5M
b) P+10 = 3M
then substirute all the Ps to Ms
b) P + 10 = 3M
5M +10 = 3M
5M - 3M = -10
this is how far as i've gone...it seems that this is wrong since there is a negative number.. Please help me. Thank you.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Here's your work. You had a very good start on the problem:
.
let P be Perla's age and M be Marilou's age <=== good. Your selection of P for Perla's age
and M for Marilou's age helps you to identify the ages better than X and Y or some other letters.
a) P = 5M <=== this is correct
b) P+10 = 3M <=== your mistake is here.
.
In 10 years, Perla's age will be P + 10, just as you showed on the left side. But Marilou
will have aged 10 years also, so her age at that time will be M + 10. So three times her age
at that time would make the equation become:
.
P + 10 = 3(M + 10)
.
and you can simplify this by multiplying out the right side to get:
.
P + 10 = 3M + 30
.
Get rid of the 10 on the right side by subtracting 10 from both sides to get:
.
P = 3M + 20
.
But up in step a) you found that P = 5M. So you can substitute 5M for P and the equation is:
.
5M = 3M + 20
.
Get rid of the 3M on the right side by subtracting 3M from both sides. This makes the
equation reduce to:
.
2M = 20
.
and solve for M (which is Marilou's present age) by dividing both sides by 2 to get:
.
M = 10
.
So Marilou is presently 10 years old.
.
and since Perla is 5 times older than Marilou, Perla is 5*10 or 50 years old.
.
Ten years from now Perla will be 60 years old. And 10 years from now Marilou will be
20 years old. And sure enough, in 10 years Perla's age (60) will be three times Marilou's
age (20). So this answer checks.
.
Your thinking was right on ... you just made a very common error ... you forgot that Marilou's
age went up by 10 years also. That's an easy mistake to make, but now you should have the idea.
.
Keep up the good work ... you've got the basic idea of how to do these problems and with
a little practice you'll be good at it.
.
Hope this helps.
.
|
|
|
