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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