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Tobys piggy bank contains only 5c and 10c coins. If it contains 65 coins with a total value of $3.80, find the number of each type of coin. Let x and y be the number of 5c and 10c coins respectively. Use the fact that the total number of coins is 65 to set up equation 1. Write the equation in the form ax+by=c

 Jun 6, 2019
 #1
avatar+101871 
+3

x + y  = 65    ⇒  y = 65 - x      (1)

5x + 10y = 380      (2)

 

Sub (1) into (2)  for  y    and we have that

 

5x + 10 ( 65 - x)  = 380    simplify

5x + 650 - 10x = 380

-5x + 650 = 380        subtract 650 from each side

-5x = -270       divide both sides by -5

x = 54 = the number of 5 cent coins

And 65 - x  =  65 - 54  = 11 = the number of 10 cent coins

 

 

cool cool cool

 Jun 6, 2019
 #2
avatar+8437 
+3

The total number of coins is  65

 

x + y  =  65       ←This is equation 1

 

The total value of the coins is $3.80

 

the total number of cents  =  380

 

5x + 10y  =  380       ←This is equation 2

 

From equation 1 we know...

 

x + y  =  65

 

x  =  65 - y

 

From equation 2 we know...

 

5x + 10y  =  380

                                         We know  x  =  65 - y  so we can substitute  65 - y  in for  x

5( 65 - y ) + 10y  =  380

                                         Distribute  5  to the terms in parenthesees.

325 - 5y + 10y  =  380

                                         Subtract  325  from both sides.

-5y + 10y  =  380 - 325

                                         Combine like terms.

5y  =  55

                                         Divide both sides by  5

y  =  11

 

Again from equation  1  we know....

 

x  =  65 - y

                           And we just determined that  y = 11

x  =  65 - 11

 

x  =  54

 Jun 6, 2019

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