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Sharing

Real life problems involving sharing which can be solved using algebra. Adapted from 'A First Book in Algebra' by Wallace Boyden

Level 1 | Level 2 | Description of levels | Help | More Algebra | More Ratio

This is level 2; Find one of three numbers given the connection between them. You can earn a trophy if you get at least 9 questions correct.

1. A man bought a hat, a pair of boots, and a tie for £90; the hat cost four times as much as the tie, and the boots cost five times as much as the tie. What was the cost of the tie?	Working:
2. A man travelled 90km in three days. If he travelled twice as far the first day as he did the third, and three times as far the second day as the third, how far did he go on the third day?	Working:
3. James had 30 marbles. He gave a certain number to his sister, twice as many to his brother, and had three times as many left as he gave his sister. How many did he have left?	Working:
4. A farmer bought a horse, cow, and sheep for £900. If he paid three times as much for the cow as for the sheep, and five times as much for the horse as for the sheep, what was the price of the cow?	Working:
5. Abdul had seven times as many apples, and Betsy three times as many as Colin had. If they all together had 55 apples, how many apples did Betsy have?	Working:
6. A man left £1400 to be distributed among three sons in such a way that James was to receive double what John received, and John double what Henry received. How much did James receive?	Working:
7. There are 120 pigeons in three flocks. In the second there are three times as many as in the first, and in the third as many as in the first and second combined. How many pigeons in the third flock?	Working:
8. Divide 209 into three parts so that the first part shall be five times the second, and the second three times the third. What is the first part?	Working:
9. Three people, A, B, and C, earned £1100; A earned four times as much as B, and C earned as much as both A and B. How much did A earn?	Working:
10. Share 770 in the ratio 5:8:9. What is the middle share?.	Working:
11. Share 306 in the ratio 5:6:7 then add the smaller share to the larger share.	Working:
12. A cistern, containing 1800 litres of water, is emptied by three pipes in two hours. Pipe one discharges three times as many litres per hour as pipe two and six times as many as pipe three. How much water does pipe one discharge in an hour?	Working:

This is Sharing level 2. You can also try

Instructions Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help. When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

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Description of Levels

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Level 1 - Find two values given their ratio and either their sum or difference

Level 2 - Find one of three numbers given the connection between them

Example for level 2

There are three numbers whose sum is 96; the second is three times the first, and the third is four times the first. What are the numbers?

Let x represent the first number,
3x represent the second number,
4x represent the third number.
x + 3x + 4x=96
8x=96
x=12
3x=36
4x=48
The numbers are 12, 36, and 48.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly.

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