Question 1036234
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


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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


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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.


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Final Answer: Chuck got 9 hits and 20 misses