At the North fair you earn 9 points for each bull’s eye you hit, but u lose 7 points for each miss. After 25 tries ,Linda has 33 points . How many did she have?

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Answer 1 · 2018-02-13T22:47:33

See a solution process below:

We can solve this using a system of equations.

Let's call the number of "hits": #h#
And the number of "misses": #m#

Then from the information in the problem we can write two equations:

Equation 1: We know the number of tries so we can write:

#h + m = 25#

Equation 2: We also know how much each hit and miss is worth and the total number of points Linda has so we can write:

#9h - 7m = 33#

Step 1) Solve the first equation for #h#:

#h + m - color(red)(m) = 25 - color(red)(m)#

#h + 0 = 25 - m#

#h = 25 - m#

Step 2) Substitute #(25 - m)# for #h# in the second equation and solve for #m#:

#9h - 7m = 33# becomes:

#9(25 - m) - 7m = 33#

#225 - 9m - 7m = 33#

#225 + (-9 - 7)m = 33#

#225 + (-16)m = 33#

#225 - 16m = 33#

#225 - color(red)(225) - 16m = 33 - color(red)(225)#

#0 - 16m = -192#

#-16m = -192#

#(-16m)/color(red)(-16) = (-192)/color(red)(-16)#

#(color(red)(cancel(color(black)(-16)))m)/cancel(color(red)(-16)) = 12#

#m = 12#

Step 3) Substitute #12# for #m# in the solution to the first equation at the end of Step 1 and calculate #h#:

#h = 25 - m# becomes:

#h = 25 - 12#

#h = 13#

Linda Had: 13 "hits" and 12 "misses"