Page 96 - Mathematics

7. When the difference between 24 and m is multiplied by 5, the result is
–20. Find the value of m .
8. One-third of a certain number is added to three-fifths of the same number
to give the sum of 14. Find the number.
9. The product of half of a certain number and 6 is 48. Find the number.

10. The sum of a number and its 40 percent is 28. Find the number.
11. A mother is 28 years older than her daughter. After 10 years, the mother
will be three times older than her daughter. Find their present ages.
12. A boy bought y balls at 500 Tanzanian shillings each. This number of
balls could decrease by 4 if the price for each ball were 700 Tanzanian
Tanzania Institute of Education
shillings each. Find the value of .y

13. When a number is multiplied by 8 and 9 is subtracted from the product,
the result is 45 more than twice the number. Find the number.
14. Julius is four times older than Amina. Five years ago, the sum of their
ages was 50. Find their present age.

15. If 18 is decreased by the sum of a number and 4, the result is 2 less than
3 times the number. Find the number.

Linear simultaneous equations
Linear simultaneous equations, also referred to as a system of linear equations, are
two or more algebraic equations which share the variables and the solutions. They
are called simultaneous equations because they are solved at once (simultaneously)
and have common solution. Consider the following linear equation.

y
x += 20 (1)
Equation (1) involves two unknowns x and .y Different values of x and y can
be used to make the equation true. The values of x and y that satisfy equation
(1) in ordered pairs (x, y) are (1,19), (2,18), (3, 17), (10,10), (13.4, 6.6) and so
on. Therefore, in order to get unique values of x and y in equation (1), another
Mathematics Form One It is possible to use equation (1) and (2) to find the unique values of x and y
linear equation is needed. For instance, if it is also known that
8 (2)
y
x −=

which satisfy both equations. These equations are such that the value of x in
equation (1) is the same as the value of x in equation (2) and the same applies
to ,y that is, the equations have common solution.

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Mathematics form 1.indd 90