can someone help me solve this math problem?

Question

ok, im really having a hard time when it comes to word problems. can someone show me how its done. thank you!

1. A pay phone is holding its maximum number of 500 coins consisting of nickels, dimes, and quarters. the number of quarters is twice the number of dimes. if the value of all the coins is $88.00, hom many nickels were in the pay phone?

2. Florian Rousseau, from Italy, won a gold medal in cycling during the 1996 Summer Olympics. Supose he rides a ci-cycle up a mountain trail at 8 miles per hour and down at same trail at 12 mph. Find the round-trip distance traveled if the total travel time was 5 hours.

z = 2y

.05x + .10y + .25z = 88.00 im still stuck here
is it gonna be .05x = 88.00 - 60y or what?

Answer 1

I'll only do number one for you
Let
x = #of nickels
y = # of dimes
z = # of quarters

x + y + z = 500

z = 2y

.05x + .10y + .25z = 88.00

Solve the Equations

.05x + .10y +.25(2y)

x + y + z = 500

x = 500 - 3y

.05(500-3y) +.10y + .50y = 88.00

25 +.45y = 88.00

.45y = 63

y = 140

Therefore

z =280

x = 500 - 140 - 280
x = 80

so you have

x = 80 nickels
y = 140 dimes
z = 280 quarters

To check

80 nickels = 4$
140 dimes = 14$
280 quarters = 70$
---------------------------

Total is 88$

I did it right YAY!

Answer 2

Let the no. of dimes be x
the no. of number of quarters is 2x . And the number of nickels would be 500-x-2x=500-3x
Their values would be respectively
Dimes=10x cents
Quarters=50 x cents,and
Nickels=5(500-3x)=2500-15x cents
According to the problem,
10x+50x+2500-15x=8800
#2 If the round trip distance was 2 miles(i.e 1 mile up and 1 mile down),he would have taken 1/8+1/12=5/24 hrs. to make the trip
Therefore the round trip distance=5/(5/24) X2=48 miles
That means 24 miles up and 24 miles down
=>45x=8800-2500=6300
=>x=6300/45=140
the no of dimes is 140
the no of quarters is 140*2=280 and
the no of nickels is 500-(140+280)=80
The two answers have got jumbled up.The last 5 lines belong to question no 1

Answer 3

Let
n = # of nickles
d = # of dimes
q = # of quarters
Then
n + d + q = 500
q = 2d
5n + 10d + 25q = 8800
n + d + 2d = 500
n + 3d = 500
5n + 10d + 50d = 8800
5n + 60d = 8800
5n + 15d = 2500
45d = 6300
d = 140
q = 280
n = 80

d/8 + d/12 = 5
3d + 2d = 120
5d = 120
d = 24 mi
2d = 48 mi

Answer 4

2. the total round trip distance was 48 miles.

You'll have to do some fiddling around with the number of coins.

Answer 5

2x + 2y = 20 utilising the simultaneous technique 2x - 2y = 4 ____________ 4x = 24 ( divide through 4) x = 6 change x in between both equations 2x + 2y = 20 2 (6) + 2y = 20 12 +2y = 20 2y = 20 - 12 2y = 8 (divide through 2) y = 4 answer : X = 6 , Y = 4

Answer 6

1)
.05(nickles)+.10(dimes)+.25(quarters)=88.00
(quarters)=2(dimes)

2)
i always hated these problems... i can do advanced calculus, but simple math kicks my ***

Answer 7

try doing your own homework!