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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 1; Find two values given their ratio and either their sum or difference. You can earn a trophy if you get at least 9 questions correct.

1. The larger of two numbers is twice the smaller, and the sum of the numbers is 129. What is the smaller number?	Working:
2. A man bought a horse and carriage for £500, paying three times as much for the carriage as for the horse. How much did the carriage cost?	Working:
3. Two brothers, counting their money, found that together they had £186, and that John had five times as much as Charles. How much did John have?	Working:
4. Divide the number 64 into two parts so that one part shall be seven times the other. What is the smaller part?	Working:
5. A man walked 24 miles in a day. If he walked twice as far in the morning as in the afternoon, how far did he walk in the afternoon?	Working:
6. For 72 cents Matthew bought some needles and thread, paying eight times as much for the thread as for the needles. How much did he pay for the thread?	Working:
7. In a school there are 672 pupils. If there are twice as many boys as girls, how many boys are there?	Working:
8. Find the first of two numbers such that their difference is 250 and the first is eleven times the other.	Working:
9. James gathered 12kg of nuts more than Henry gathered. What weight of nuts did Henry gather if James gathered three times as many as Henry?	Working:
10. A house cost £80000 more than a plot of land, and five times the cost of the plot equals the cost of the house. What was the cost of the house?	Working:
11. Mr Meaner is 48 years older than his son, but he is only three times as old. How old is Mr Meaner?	Working:
12. The sum of two numbers is 4256, and one is 37 times the other. What is the larger number?	Working:

This is Sharing level 1. 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 1

The sum of two numbers is 60, and the larger number is four times the smaller. What are the numbers?

Let x represent the smaller number;
then 4x represents the larger number,
and 4x+x=60,
or 5x=60;
therefore x=12,
and 4x=48.
The numbers are 12 and 48.

Second Example. If the difference between two numbers is 48, and one number is five times the other, what are the numbers?

Let x represent the smaller number;
then 5x represents the larger number,
and 5x-x=48,
or 4x=48;
therefore x=12,
and 5x=60.
The numbers are 12 and 60.

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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