SOLUTION: Hi A bottle contains quarters dimes nickels and pennies. The ratio of quarters to dimes is 8 to 3. Nickels to quarters is nine to five . Pennies to quarters is 7 to 2. The total v

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Question 1182112: Hi
A bottle contains quarters dimes nickels and pennies. The ratio of quarters to dimes is 8 to 3. Nickels to quarters is nine to five . Pennies to quarters is 7 to 2. The total value of the coins is $16.50. How many coins of each kind are there.
Thanks
Found 4 solutions by josgarithmetic, ikleyn, MathLover1, greenestamps:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Write the ratios and make each coin count in terms of q, quarters.
.
.
q=40 from equation all in terms of just q for quarters.

d=15
-
b=72
-
p=140

Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!
.
A bottle contains quarters dimes nickels and pennies.
The ratio of quarters to dimes is 8 to 3.
Nickels to quarters is nine to five .
Pennies to quarters is 7 to 2.
The total value of the coins is $16.50. How many coins of each kind are there.
~~~~~~~~~~~~~~~~~~~ 

From the condition, we have these ratios


    D%2FQ = 3%2F8

    N%2FQ = 9%2F5

    P%2FQ = 7%2F2


The common denominator is 8*5 = 40.

So, we can rewrite these fraction in EQUIVALENT WAY using the common denominator of 40


    D%2FQ = 15%2F40

    N%2FQ = 72%2F40

    P%2FQ = 140%2F40


Having these fractions and denoting the number of quarters as 40x, we have


    - the number of dimes   is 15x.

    - the number of nickels is 72x.

    - the number of pennies is 140x.


We then write the total money equation


    25*(40x) + 10*(15x) + 5*(72x) + 1*(140x) = 1650 cents, in total.


Simplify and find x

    1000x + 150x + 360x + 140x = 1650

    (1000 + 150 + 350 + 140)x  = 1650

               1650x           = 1650.


Then x = 1 and the ANSWER  is  40 quarters, 15 dimes, 72 nickels and 140 pennies.

Solved.



Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The ratio of quarters to dimes is 8 to 3.
q%2Fd=8%2F3=>d=q%2F%288%2F3%29 =>d=3q%2F8+
Nickels to quarters is 9 to 5.
n%2Fq=9%2F5=>n=+9q%2F5+
Pennies to quarters is 7 to 2.
p%2Fq=7%2F2=> p=7q%2F2
The total value of the coins is $16.50.
0.25q%2B0.10d%2B0.05n%2B0.01p=16.50
0.25q%2B0.10%283q%2F8%29%2B0.05%289q%2F5%29%2B0.01%287q%2F2%29=16.50
0.25q%2B0.0375q%2B0.09q%2B0.035q=16.50
0.4125q=16.50
q=16.50%2F0.4125
q=40
then
d=3q%2F8 =>d=%283%2A40%29%2F8+=3%2A5=15
n=+9q%2F5 =>n=+%289%2A40%29%2F5+=9%2A8=72
p=7q%2F2=>p=%287%2A40%29%2F2=7%2A20=140
there are:
40 quarters
15 dimes
72+ nickels
140 pennies

Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


The first tutor showed the answer without showing anything that would teach you how to get that answer.

The other two tutors used a perfectly good method of solving the problem by writing fractions to represent the given ratios and then working with those fractions.

I prefer a different method, explained below. Try both methods and see what "works" for you.

The given ratios are
Q:D = 8:3
N:Q = 9:5
P:Q = 7:2

All three ratios involve Q, the number of quarters. So multiply each of the given ratios by appropriate constants to make Q the same number in all three ratios.

Q is 8 in the first ratio and 5 in the second; so multiply the first ratio by 5 and the second by 8 to make Q 40 in both.

Q:D = 8:3 = 40:15
N:Q = 9:5 = 72:40

Then multiply the third ratio by 20 to make Q=40 in that ratio also.

P:Q = 7:2 = 140:40

Now we can write a single ratio comparing all four quantities:

N:Q:D:P = 72:40:15:140

Having that, we can write the numbers of the different coins as
nickels: 72x
quarters: 40x
dimes: 15x
pennies: 140x

This is the same point the other method of solution got to, so solve the problem from there as shown in the other responses.

So the method I used gets you to exactly the same place the other method does; it just gets you there by a different method that I like to use.

So as I said earlier, try both methods for solving similar problems and find what works best for you.