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
