Linear equation question

[KLin]

So a friend of mine showed me this problem on his homework, and I was totally stumped by part D of the question. See below

Exercise Heart Rate To achieve the maximum benefit for
the heart when exercising, your heart rate (in beats per
minute) should be in the target heart rate zone. The lower
limit of this zone is found by taking 70% of the difference
between 220 and your age. The upper limit is found by
using 85%.


d. Two women in an aerobics class stop to take their pulse,
and are surprised to find that they have the same pulse.
One woman is 36 years older than the other and is working
at the upper limit of her target heart rate zone. The
younger woman is working at the lower limit of her target
heart rate zone. What are the ages of the two women,
and what is their pulse?

How the hell do you find the values in part D with only having 2 linear equations? I figured the equation for the younger woman is y = .7(220-x) or y = -.7x+154 and for the older lady it's y = .85(220-(x+36)) or y = -.85x + 184. Are those the correct equations? Like I said, we were totally stumped. I haven't done this stuff since 10th grade. any ideas?

 

[Random Variable]

You don't know how to solve a 2x2 linear system?

 

[KLin]

Originally posted by: Random Variable
You don't know how to solve a 2x2 linear system?

Obviously not. Like I said, I haven't done this stuff in like 10 years.

 

[Random Variable]

-.7x+154 = -.85x + 184
0.15x=30
x=200

y=14

 

[OdiN]

I almost said do your own damn homework...but then I realized that you probably don't have any

 

[Syringer]

You're close, you just have it backwards.

Let X be the older woman's age.
So X+36 = younger woman's age.

.85 (220-x) --> 85% of 220 - older woman's age
.7 (220 - (x+36)) --> 70% of 220 - younger woman's age

Set them equal and solve for x.

Answers are 52 and 26.

 

[KLin]

Originally posted by: Syringer
You're close, you just have it backwards.

Let X be the older woman's age.
So X+36 = younger woman's age.

.85 (220-x) --> 85% of 220 - older woman's age
.7 (220 - (x+36)) --> 70% of 220 - younger woman's age

Set them equal and solve for x.

Answers are 52 and 26.

Actually 16 . I cheated in excel to find the answer, the heart rate is also 142.8. But for some reason, I can't get the right value for X when I set the equations equal to each other.

 

[Syringer]

Er, yeah. I wrote 16 down when I solved it but my writing is so bad the 1 looked like a 2

 

[KLin]

Originally posted by: Syringer
You're close, you just have it backwards.

Let X be the older woman's age.
So X+36 = younger woman's age.

.85 (220-x) --> 85% of 220 - older woman's age
.7 (220 - (x+36)) --> 70% of 220 - younger woman's age

Set them equal and solve for x.

Answers are 52 and 26.

One more thing, shouldn't it be X-36 = younger woman's age?

 

[Syringer]

D'oh, yeah you're right.

On my calculator I put 220-x+36 without the parentheses around x+36 so it actually worked out

 

[KLin]

I finally got the answer out. Thanks for the help Everyone :thumbsup:. I think I need to take some math classes to get myself back up to speed.