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Author:
Michele Harris

The student will be able to use linear equations to solve word problems.

Solving word problems using linear equations.

Tutorial

Justin and his father went fishing and together caught 12 fish. Three times the number of fish that Justin caught exceeds 12 by as much as 5 times the number that his father caught exceeds 8. How many fish did each catch?

*start by setting up your notes for Justin and his father. What do you know about each?

Justin - "3 times the number of fish that Justin caught exceeds 12"

This means we can represent Justin as: 3x - 12

"by as much as" - this means we set Justin equal to father

father - "5 times the number his father caught exceeds 8"

This can be represented as: 5(12 - x) - 8

Source: ABEKA Algebra 1 2002

Your equation should be: 3x - 12 = 5 (12 - x) - 8

Justin = 8

father = 4

Source: ABEKA Algebra 1 2002

In a baseball game 1/2 the number of runs scored by the winning team exceeds 5 by as much as 1/3 the losing team's runs exceeds 1. If the total runs scored is 18, what is the final score?

*think through the problem carefully, using the same thought process as in the previous problem.

Source: ABEKA Algebra 1 2002

x = winning team

18 - x = losing team

your equation should read: 1/2x - 5 = 1/3 (18 - x) - 1

answer: 12 to 6

Source: ABEKA Algebra 1 2002

A man paid $8.50 for a small pump and 5 feet of tubing. He paid 12 times as much for the pump as for each foot of tubing. How much did the pump cost? The tubing?

*x = how much he paid for the tubing

therefore, he paid 5x for the tubing ( bought 5 feet) and 12x for the pump (because he paid 12 times as much as he did for the tubing)

$8.50 is the total he paid for all

Source: ABEKA Algebra 1 2002

your equation should look like this:

8.50 = 5x + 12x

pump = $6.00

tubing = $2.50

Source: ABEKA Algebra 1 2002

In lighting a parking lot, a certain number of 500-watt bulbs and twice as many 250-watt bulbs were used. The total illumination amounted to 5,000 watts. Find the number of bulbs of each kind used.

x = number of bulbs

Source: ABEKA Algebra 1 2002

your equation should be:

500x + 2(250x) = 5000

we multiplied 250x by 2 because there were twice as many bulbs this size.

answer: 500-watt = 5

250-watt = 10

Source: ABEKA Algebra 1 2002

At the town waterworks, 2 large pumps and 4 smaller ones delivered 4800 gallons of water a minute. *Each of the large pumps delivered 4 times as much water as each small pump.* How many gallons per minute did each pump deliver?

small = x

large = 4x

Source: ABEKA Algebra 1 2002

2 (4x) + 4 (x) = 4800

small = 400 gallons

large = 1600 gallons

Source: ABEKA Algebra 1 2002

At target practice an artillery crew made 11 hits in less than a minute. If 3/4 of the number of rounds fired was 9 times the number of misses, how many rounds were fired?

x = fired

x- 11 = misses

Source: ABEKA Algebra 1 2002

your equation should look like this:

3/4x = 9 (x - 11)

12 rounds fired

Source: ABEKA Algebra 1 2002

A playground is 101 feet longer than it is wide. If its width were decreased 25 feet, its length would be twice its width. Find the dimensions of the playground.

w = width

w + 101 = length

w - 25 = new width

Source: ABEKA Algebra 1 2002

your equation should look like:

w + 101 = 2 (w - 25)

You are setting the old length equal to the new length

The dimensions are: 151 ft by 252 ft

Source: ABEKA Algebra 1 2002

A man invests 4/5 of his capital at 10 1/2% and the rest at 10%. His annual income is $416. Find his capital.

x = amount of capital

4/5x = 10 1/2%

1/5x = 10% ........... 1/5 because that is what is left after taking 4/5 for first percentage

Source: ABEKA Algebra 1 2002

your equation should look like:

.105 (4/5x) + .10 (1/5x) = 416

His capital is $4000

Source: ABEKA Algebra 1 2002

In a balloon race, the sum of the distances covered by two of the balloons was 1,025 miles. If the distance covered by the first balloon was 50 miles more than 1/2 of that covered by the second balloon, how far did each travel?

*d= second balloon

1/2d + 50 = first balloon

Source: ABEKA Algebra 1 2002

Your equation should look like this:

d + 1/2d + 50 = 1025

answers: 375 miles; 650 miles

Source: ABEKA Algebra 1 2002

A cashier saves 1/5 of her monthly gross salary. This is $40 more than is saved by her friend, a secretary, whose monthly gross salary is $200 greater. If the secretary saves 1/7 of her salary, find how much each earns per month.

*x = monthly salary for secretary

x - 200 = cashier

Source: ABEKA Algebra 1 2002

your equation should look like:

1/5 (x - 200) - 40 = 1/7x

cashier: $1200

secretary: $1400

Source: ABEKA Algebra 1 2002