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Question 590798: I am having a terrible time doing word problems in algebra, simple for some but not for me. Could someone please help with two problems, thank you very much.
A university bookstore recently sold a wire bound graph-paper notebook for $2.50, and a college-ruled notebook for $2.30. At the start of spring semester, a combination of 50 of these notebooks were sold for a total of $118.60. How many of each type were sold?
A bricklayer and an electrician together spend 90 hours working on a new house. If the bricklayer earns $12 per hour, the electrician earns $16 an hour, and the owner pays them a total of $1350 for their work, how many hours does each worker spend on the house?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! A university bookstore recently sold a wire bound graph-paper notebook for $2.50, and a college-ruled notebook for $2.30. At the start of spring semester, a combination of 50 of these notebooks were sold for a total of $118.60. How many of each type were sold?
w = number of wire bound notebooks.
c = number of college ruled notebooks.
total of 50 notebooks were sold for $118.60.
your equations are:
2.50w + 2.30c = 118.60
w + c = 50
these are 2 equations that need to be solved simultaneously.
you can use substitution.
from the second equation, solve for w to get:
w = 50 - c
substitute for w in the first equation to get:
2.50*(50-c) + 2.30c = 118.60
simplify to get:
125 - 2.50c + 2.30c = 118.60
combine like terms to get:
125 - .20c = 118.60
subtract 125 from both sides of the equation to get:
.20c = -6.4
divide both sides of the equation by -.20 to get:
c = -6.4/-.20 = 32
since w + c = 50, this means that w equals 18.
you have w = 18 and c = 32
w + c = 18 + 32 = 50
2.50*w + 2.30*c = 118.60 becomes:
2.50*18 + 2.30*32 = 118.60
answer is good.
18 wire bound notebooks are sold
32 college ruled notebooks are sold.
A bricklayer and an electrician together spend 90 hours working on a new house. If the bricklayer earns $12 per hour, the electrician earns $16 an hour, and the owner pays them a total of $1350 for their work, how many hours does each worker spend on the house?
x = number of hours the bricklayer works
y = number of hours the electrician works
x + y = 90
12x + 16y = 1350
you have 2 equations that need to be solved simultaneously.
you can solve by substitution.
solve for y in the first equation to get:
y = 90 - x
substitute for y in the second equation to get:
12x + 16*(90-x) = 1350
simplify to get:
12X + 1440 - 16X = 1350
combine like terms to get:
-4x + 1440 = 1350
subtract 1440 from both sides of the equation to get:
-4x = 1350 - 1440 = -90
divide both sides of the equation by -4 to get:
x = 22.5
since x + y = 90, this means that y is equal to 90 - 22.5 = 67.5
x = 22.5
y = 67.5
x + y = 90
12*x + 16*y = 1350
12*22.5 + 16*67.5 = 270 + 1080 = 1350
answers are good.
bricklayer works 22.5 hours
electrician works 67.5 hours
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