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+5
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4
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the bowl had $2.70 in pennys and Nickles. if there were 54 more pennies than nickles in the bowl how many were pennies and how manny were Nickles?

 Mar 15, 2016

Best Answer 

 #4
avatar
+10

Solve the following system:
{n+54 = p
0.05 n+0.01 p = 2.7

In the first equation, look to solve for p:
{n+54 = p
0.05 n+0.01 p = 2.7

n+54 = p is equivalent to p = n+54:
{p = n+54
0.05 n+0.01 p = 2.7

Substitute p = n+54 into the second equation:
{p = n+54
0.05 n+0.01 (n+54) = 2.7

0.05 n+0.01 (n+54) = 0.05 n+(0.01 n+0.54) = 0.06 n+0.54:
{p = n+54
0.06 n+0.54 = 2.7

In the second equation, look to solve for n:
{p = n+54
0.06 n+0.54 = 2.7

0.06 n+0.54 = (3 n)/50+27/50 and 2.7 = 27/10:
(3 n)/50+27/50 = 27/10

Subtract 27/50 from both sides:
{p = n+54
(3 n)/50 = 54/25

Multiply both sides by 50/3:
{p = n+54
n = 36

Substitute n = 36 into the first equation:
{p = 90
n = 36

Collect results in alphabetical order:
Answer: |  n = 36                  and                p=90
 

 Mar 15, 2016
 #1
avatar+1491 
+4

Okay so Katie you understand how make an system out of this correct?

 

If so I'll show you my method of solving these types of problems.

 

Instead of thinking of it as money I think of the pennies and nickels as a value of .01 and .05, respectively. The total amount will take the value of 2.70.

 

So in order to solve a problem like this you need a system.

 

Let "p" be pennies and "n" be nickels.

 

If the total amount of pennies and nickels have a value of 2.70 and there are 54 more pennies than nickels you'll get a system like this:

 

n + 54 = p

n(0.05) + p(0.01) = 2.70

 

Now I think I should leave the rest to you. If you don't know systems let me know.

 Mar 15, 2016
 #2
avatar+545 
+5

okay thank you I do know systems I just didn't know the formula for this problem thank you that helps

 Mar 15, 2016
 #3
avatar+128090 
0

Very nice, HSC.......!!!!!

 

 

 

 

cool cool cool

 Mar 15, 2016
 #4
avatar
+10
Best Answer

Solve the following system:
{n+54 = p
0.05 n+0.01 p = 2.7

In the first equation, look to solve for p:
{n+54 = p
0.05 n+0.01 p = 2.7

n+54 = p is equivalent to p = n+54:
{p = n+54
0.05 n+0.01 p = 2.7

Substitute p = n+54 into the second equation:
{p = n+54
0.05 n+0.01 (n+54) = 2.7

0.05 n+0.01 (n+54) = 0.05 n+(0.01 n+0.54) = 0.06 n+0.54:
{p = n+54
0.06 n+0.54 = 2.7

In the second equation, look to solve for n:
{p = n+54
0.06 n+0.54 = 2.7

0.06 n+0.54 = (3 n)/50+27/50 and 2.7 = 27/10:
(3 n)/50+27/50 = 27/10

Subtract 27/50 from both sides:
{p = n+54
(3 n)/50 = 54/25

Multiply both sides by 50/3:
{p = n+54
n = 36

Substitute n = 36 into the first equation:
{p = 90
n = 36

Collect results in alphabetical order:
Answer: |  n = 36                  and                p=90
 

Guest Mar 15, 2016

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