Question

Can you answer question 45 and 46? (Show work)

Answer 1

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

$h + m = 30$

+5 for a hit, -10 for a miss, John lost 90 translates to

$5h + -10 m = -90$

We have

$m = 30 - h$

$5h - 10(30 -h) = -90$

$5h - 300 + 10h = -90$

$15h = 210$

$h = 210/15 = 14$

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 ...

$b + c = 12$

... 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.

$8c + 10b = 12(8.50) = 102.00$

The solving is pretty much just like the last one; we eliminate the unknown we're not asked for.

$b = 12 - c$

$8c + 10(12 - c) = 102$

$-2c = 102 - 120 = -18$

$c = 9$

Answer: 9

Check: (9(8)+10(3))/12=102/12 = 8.50 good