Download Problems Involving Simultaneous Equations

Problems Involving Simultaneous Equations
To solve worded problems read the question carefully and define the two variables.
Formulate two equations from the information given and number them.
Use either the elimination method or the substitution method to solve the two
equations simultaneously.
Check your answer by: substituting the values obtained for each variable into
the original equations or using a graphics calculator.
Write the following as equations and solve.
1. Richy got better results for his maths test than for his English test. If the sum of his two
marks is 163 and the difference is 31, find the mark for each subject.
2. Find two numbers whose difference is 5 and whose sum is 11.
3. The difference between two numbers is 2. If three times the larger number minus
double the smaller number is 13, find the two numbers.
4. One number is 9 less than three times a second number. If the first number plus twice
the second number is 16, find the two numbers.
5. A rectangular house has a perimeter of 40 metres and the length is 4 metres more
than the width. What are the dimensions of the house?
6. Gina went to buy some nuts and bolts to finish a project. She did not buy the same
number of nuts and bolts, as some of the bolts needed two nuts each. She bought 30
nuts and bolts in total. If each nut cost 10 cents, each bolt 20 cents and the total
purchase cost was $4.20, how many nuts and how many bolts did she buy?
7. Ken has 5 lemons and 3 oranges in his shopping trolley, and the cost of the fruit is
$3.50. Barbie, with 2 lemons and 4 oranges, pays $2.10 for her fruit. How much does
each type of fruit cost?
8. A surveyor measuring the dimensions of a block of land finds that the length of the
block is three times the width. If the perimeter is 160 metres, what are the dimensions
of the block?