A very annoying question?

Question

This is one of those questions where you have to figure out how much a person bought of each thing to have a certain final bill.


Wayne is building a shed in his backyard to store his snowmobile. "Value Hardware" sells 3-in finishing nails for $0.99/lb and 2-in finishing nails for $1.39/lb.

Wayne needs 5 lbs. of nails. If his bill totals $6.15, how many pounds of each size did he buy?


Please show me how to solve this problem and the other kinds like these!!! They are so frustrating!

Answer 1

Let
p₁- price of the 1st item
p₂- price of the 2nd item
c – total cost
a₁- amount of the 1st item
a₂- amount of the 2nd item
a – total amount

Generally, from the equations
a₁+ a₂= a
p₁a₁+ p₂a₁= c
you may find any 2 unknowns if other 4 are known.

Just replace letters by numbers and solve the equations.
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Answer 2

Let's say Wayne bought N pounds of the 3-inch nails. If he bought 5 lbs total, then he must have bought 5 - N of the two-pound nails. If the 3-in nails cost $0.99 per pound, then he spend 0.99N on them. If the 2-in nails cost $1.39 per pound, then he spent 1.39(5-N) on them. Combined, we know it cost him $6.15. So:
0.99N + 1.39(5-N) = 6.15

Solve this for N, and then use N to find 5 - N. This gives you the amount of pounds for each nail type, respectively.

Answer 3

x=3-in finishing nails
y= 2-in finishing nails
x+y =5
0.99x + 1.39y =6.15
x=2 y=3