Problem 1 :
It took Thomas 25 minutes longer to do his math homework than to do his French homework. He spent a total of 2.25 hours on both subjects. How much time did he spend on math?
Solution :
Let x be the time taken to complete his French homework.
Time taken to complete math homework = (x + 25) minutes
Total time spent for both subjects = 2.25 hours
1 hour = 60 minutes
2.25 hours = 2.25 (60)
= 135 minutes
x + x + 25 = 135
2x + 25 = 135
2x = 135 - 25
2x = 110
x = 110/2
x = 55 minutes
Problem 2 :
Jesse earns $6 an hour babysitting for his younger brother. His mom gave him $71 last week. This included his babysitting money and his $20 allowance. How many hours did Jesse babysit?
Solution :
Number of hours she is taking for baby sitting = x
Amount she receives for one hour of babysitting = 6
Her allowance = 20
6x + 20 = 71
6x = 71 - 20
6x = 51
x = 51/6
x = 17/2
x = 8.5
So, she is receiving $8.5 for one hour of babysitting.
Problem 3 :
Carol and Cathy are each saving money for a vacation. Carol started with $25 and saves $7.50 a week. Cathy started with $10 and saves $10 a week. When will they have saved the same amount?
Solution :
Let x be the number of weeks that they are saving.
Amount saved by Carol = 25 + 7.50 x
Amount saved by Cathy = 10 + 10x
They are saving the same amount, then
25 + 7.50x = 10 + 10x
25 - 10 = 10x - 7.50x
15 = 2.50x
x = 15/2.50
x = 6
So, at the end of the 6th week they will have the same amount.
Problem 4 :
One weekend Bill earned 3 times as much as Jim. Tom earned $5 more than Jim. In all, they earned $60. How much did each earn?
Solution :
Let x be the amount Jim is earning.
Amount earned by Tim = 5 + x
Amount earned by Bill = 3x
They added together = 60
x + 5 + x + 3x = 60
5x + 5 = 60
5x = 60 - 5
5x = 55
x = 55/5
x = 11
Problem 5 :
The Maxwell children have hired a caterer to provide food for an anniversary party for their parents. The caterer has quoted a price of $96 per person and is asking for an advance payment of one-fourth of the total bill. If the advance payment is $1200, how many guests are invited to the party?
Solution :
Advance payment = 1200
Advance payment = 1/4 of total bill
Let x be the total bill
1200 = (1/4) x
1200 = x/4
x = 1200(4)
x = 4800
Price per person = $96
Let n be the number of guests.
Product of number of guests and cost spent for each person
96 n = 4800
x = 4800/96
x = 50
So, number is guests were attended the party is 50.
Problem 6 :
Three children each contributed toward a birthday present for their mother. The oldest contributed three times as much as the youngest, while the second oldest contributed 50 cents more than the youngest. If the present costs $10.50, how much did each contribute?
Solution :
Let x be the amount contributed by the youngest.
Amount contributed by oldest = 3x
Amount contributed by second oldest = 0.50
Amount in the present = 10.50
x + 3x + 0.50 = 10.50
4x = 10.50 - 0.50
4x = 10
x = 10/4
x = 2.5
Problem 7 :
At a school game, student tickets were 50 cents each and adult tickets were $1 each. If the total receipts from 900 tickets were $500, how many tickets of each kind were sold?
Solution :
Let x be the number of student tickets and 900 - x be the number of adult tickets.
Total number of tickets = 900
Total cost = 500
0.50x + 1(900 - x) = 500
0.50x + 900 - x = 500
-0.50x + 900 = 500
-0.50x = 500 - 900
-0.50x = -400
x = 400/0.50
x = 800
Number of student tickets = 800
number of adult tickets = 100
Problem 8 :
A salesman sold 200 pairs of slippers. Some were sold at $6 per pair and the remainder were sold at $11 per pair. Total receipts from this sale were $1600. How many pairs of slippers were sold at $6 each?
Solution :
Total number of pairs of slippers = 200
In which x be the number of slippers cost $6, then 200 - x number of slippers cost $11.
6x + (200 - x) 11 = 1600
6x + 2200 - 11x = 1600
-5x + 2200 = 1600
-5x = 1600 - 2200
-5x = -600
x = 600/5
x = 120
Number of slippers that cost $6 is 11.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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