SOLUTION: A game pays 7 cents for a hit and charges 5 cents for a miss. Chuck took 29 shots and lost 37 cents. How many hits and how many misses did he have? set up equation using 2 variable

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Question 1036234: A game pays 7 cents for a hit and charges 5 cents for a miss. Chuck took 29 shots and lost 37 cents. How many hits and how many misses did he have? set up equation using 2 variables.
Found 2 solutions by Edwin McCravy, jim_thompson5910:
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
Let the number of hits be x
Let the number of misses be y

                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
shot        shots      shot      shots
-------------------------------------------
hits         x       $0.07       $0.07x
misses       y      -$0.05      -$0.05y
-------------------------------------------
TOTALS      29       -----      -$0.37

 The first equation comes from the "Number of shots" column.

  

                     x + y = 29

 The second equation comes from the "Value of all shots" column.
  

            0.07x - 0.05y = -0.37

Get rid of decimals by multiplying every term by 100:

                 7x + -5y = -37

 So we have the system of equations:

           .

We solve by substitution.  Solve the first equation for y:

                                x + y = 29
                                    y = 29 - x

Substitute (29 - x) for y in 7x + -5y = -37

                       7x - 5(29 - x) = -37
                        7x - 145 + 5x = -37
                           12x + -145 = -37
                                  12x = 108
                                    x = 9 = the number of hits.

                      Substitute in y = 29 - x
                                    y = 29 - (9)
                                    y = 20 misses.

Checking:  9 hits is $0.63 and 20 miss is -$1.00
            That's 29 shots.
            And indeed $0.63 - $1.00 = -$0.37

Edwin
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
x = number of hits
y = number of misses

He took 29 shots, so the total x+y must be equal to 29. The first equation is therefore

x+y = 29

solve for y to get

y = 29 - x

-------------------------------------------

The game pays 7 cents for each hit. Chuck made x hits. So he receives 7*x cents, where x is some positive whole number. Keep this fact in mind: x cannot be some fractional or decimal value. It must be a positive whole number.

Chuck loses 5 cents for each miss. If he missed y times (y is a positive whole number) then he lost 5*y cents. A loss in mathematics is often denoted with a negative number. For instance, if you lost 5 dollars, then you'd record it in a ledger with the value -5.

Since he gains 7*x cents for the x hits and loses 5*y cents for the y losses, this means we have

7*x + (-5*y) = 7x - 5y

The expression 7x - 5y is then set equal to -37 to indicate he lost a net of 37 cents. After the gains and losses are totaled, at the end of the day, he lost 37 cents total.

So that means we have this second equation

7x - 5y = -37

------------------------------------

Let's plug y = 29 - x into the second equation and see what we get when we solve for x.

7x - 5y = -37
7x - 5(29 - x) = -37
7x - 145 + 5x = -37
12x - 145 = -37
12x - 145+145 = -37+145
12x = 108
12x/12 = 108/12
x = 9

So Chuck got 9 hits. Use this value of x to get the value of y


y = 29 - x
y = 29 - 9
y = 20

which means he got 20 misses.

============================================================================

Final Answer: Chuck got 9 hits and 20 misses
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