45. These word problems often seem to be two equations in two unknowns, here h for hits and m for misses.
"After 30 tries" translates into
[tex]h + m = 30[/tex]
+5 for a hit, -10 for a miss, John lost 90 translates to
[tex]5h + -10 m = -90[/tex]
We have
[tex] m = 30 - h[/tex]
[tex]5h - 10(30 -h) = -90[/tex]
[tex]5h - 300 + 10h = -90[/tex]
[tex]15h = 210[/tex]
[tex]h = 210/15 = 14[/tex]
Answer: 14
Check: 5(14)-10(16)=-90, good
46. We have to make the odd assumption the grocer sells for his cost, but let's not beat up the question too hard.
Again, two unknowns, b kilograms of Brazil nuts and c kilograms of cashews.
... sold 12 kg of the mixture ...
[tex]b + c = 12[/tex]
... cashews $8/kg and Brazil nuts $10/kg and the results is $8.50/kg ...
This one's a bit more involved to translate because we have to recognize the total price is the 8.50 per kg times 12 kg.
[tex]8c + 10b = 12(8.50) = 102.00[/tex]
The solving is pretty much just like the last one; we eliminate the unknown we're not asked for.
[tex]b = 12 - c[/tex]
[tex]8c + 10(12 - c) = 102[/tex]
[tex]-2c = 102 - 120 = -18[/tex]
[tex]c = 9[/tex]
Answer: 9
Check: (9(8)+10(3))/12=102/12 = 8.50 good
