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Practice in Proportional Word Problems - 7th grade

Please attempt to solve 12 problems in the attached documents. They are all word problems that provide practice in solving proportions or calculating formulas that include unknowns. The student asked for step-by-step instructions to help to understand how to solve them.


Solution Preview

See the attachments.

The hint to all of these is that you are setting up a proportion, and this always means
a y
---- = ------
b x

Where a and b are given values and y might be a given value or not, but x is always a calculated value.

Where you put the x is very important, because the units of b and x have to be the same units, either cups or inches or whatever, because you are calculating the x.

The y also must be the same units as a, so that if you end with an equation that is solved for x, the y will be in the right place in the equation.


Madeline saved $13.50 on a $45 watch during a holiday sale. Which equation can be used to find d, the amount she should save in dollars for a $70 camera on sale at the same rate of discount?

What you have is the ratio of the discount (D) for the watch and the original price (P) of the watch.

What you are given is the original price of the camera (p) and you have to calculate the discount amount for the camera (d) So your equation is:

D d
--- = -----
P p

13.50 d
-------- = -----
45 70

Now, cross multiply - this means, multiply the denominator of the first fraction by the denominator of the second fraction, then multiply the numerator of the first fraction by the denominator of the second fraction:

45d = 13.50 x 70

Divide both sides by 45

45d = 945
------ -----
45 45

Because any number divided by itself equals 1, the 45/45 equals 1, then divide 945/45, leaving you with

d = 21 This is your answer

So with the discount, Madeline would save $21 on the camera, and only had to pay $49.

* Your answer:
$13.50/$45 x 100 = 30%
$70 x .30 = $21.00

You got the answer correct for this problem, although you used a different but valid strategy to do it - you found the percentage of discount by dividing the savings by the original price, and then you multiplied that
percentage, in decimal form, by the original price for the camera.

(I won't give the answer anymore except to correct, but will always show
you how to do it)

Jason earned $84 for working 8 hours at the bank. Which equation could be used to find x,
the amount of dollars he should earn working h hours at the same rate?

84 x
----- = -------
8 h
cross multiply

84h = 8x

Divide both sides by 8

84h = 8x
---- ----
8 8

Divide 84 by 8, and the 8/8 =1, leaving you with x = your answer.

x = 84/8

* You got the method correct, by dividing 84/8 using long division. But
the answer is 10.5. Be careful when using long division to line up the
subtracted numbers and the numbers that you bring down correctly:

8 divided by 8 = 1, 1 x 8 = 8, place this 8 ...

Solution Summary

This is a description and explanation of a series of 12 mathematics proportion practice word problems, including step by step solutions on how to solve them.