Question

Langston will pay $575 to three different credit cards: Expert Card, Passport, and US Speedy. She will pay three times as much to Expert Card as US Speedy since it has a higher balance. She also expects the Passport payment to be only 15% of the total of the other two payments. How much will Langston pay towards the Passport credit card balance?

$75.00

$86.25

$125.00

$375.00

Answer 1

Let the amount paid to Expaert = e
Let the amount paid to Passport = p
Let the amount paid to US Speedy = u

e + p + u = 575
e = 3u
p = 0.15(e + u), but e = 3u, so
p = 0.15(3u + u) = 0.15(4u) = 0.6u
Substitute 3u for e and 0.6u for p and solve for u.
Then p = 0.6u

Answer 2

I'm so confused

Answer 3

What variables go into u or p or e???

Answer 4

u, p, and e are the variables.
I'll explain again more slowly.

Answer 5

The total amount paid out is $575.
Out of that, part will go to Expert, part to Passport, and part to US Speedy. Ok?

Answer 6

Okay

Answer 7

I am using the variables e, p, and u, to represent the amounts paid to Expert, Passport and US Speedy, respectively. Ok?

Answer 8

The total paid to all three cards is $575.
That means e + p + u = 575. Ok?

Answer 9

ok

Answer 10

Now we need the info they give us about how much is paid to each card.

Answer 11

ok

Answer 12

She will pay three times as much to Expert Card as US Speedy
From here we get e = 3u
ok?

Answer 13

then?

Answer 14

From here:
"She also expects the Passport payment to be only 15% of the total of the other two payments."
we get p = 15%(e + u)
ok?

Answer 15

go on

Answer 16

This expression for p can be simplified.
p = 15%(e + u)
We know that e = 3u, so let's replace e with 3u:
p = 15%(3u + u)

Answer 17

This can be simplified further:
p = 15%(3u + u)
p = 15%(4u)
p = 0.15(4u)
p = 0.6u

Answer 18

Maybe it'd be easier for me to understand if you actually did the problem without putting the answer so I can make sense of it myself, and if I have any questions I can ask.

Answer 19

We didn't get to the answer yet. We are just getting there slowly.

Answer 20

Now we go back to
e + p + u = 575
Since e = 3u, and p = 0.6u, we susbtitute in the equation:
e + p + u = 575
3u + 0.6u + u = 575
Now you can solve for u.

Answer 21

and how do i solve for u?

Answer 22

Also how did you get 0.6u

Answer 23

Add 3u plus 0.6u plus u

Answer 24

.....

Answer 25

Read above my answer that starts "This can be simplified further:"
for an explanation of 0.6u

Answer 26

Would it be 3.6u^2 = 575 ?????????

Answer 27

3u + 0.6u + u = 575
u is the same as 1u
3u + 0.6u + 1u = 575
4.6u = 575

Answer 28

So u = 125

Answer 29

yes

Answer 30

now e = 3u, so e = 3(125)

Answer 31

p = 0.6u, so p = 0.6(125)

Answer 32

So the answer would be $75

Answer 33

Yes

Answer 34

thank you!