8 Applying Algebra
The methods of algebra can be used to solve any numerical problem.
Eg Find the height of a triangle with an area of 78cm² and a base length of 6cm
formula A = ½bh
substitution 78 = ½x6h
calculate 78 = 3h
78 ÷ 3 = h
h = 26cm
8A In each question use the formula given to find:
1. the diameter of a circle with a circumference of 90cm C=pd
2. the length of a square with an area of 40cm² A=l²
3. the height of a triangle with an area of 70cm² and a base of 20cm. A=½bh
4. the height of a cuboid with a volume of 240cm³, length 15cm and width 8cm. V=lwh
5. the speed of a train which travels 160 miles in 2 hours. d=st
6. the radius of a circle with an area of 314cm² A=pr²
7. The width of a rectangle which has a perimeter of 22m and a length of 7m. P=2(l+w)
8. the acceleration of a body of mass 20kg which has a force of 150N applied to it F=ma
And even everyday problems can be solved with algebra.
Eg Find the wage of a person who works for 15 hours at £3 per hour.
W = hr Wage = hours worked x rate per hour.
W = 15x3
W = £45
How many hours must the person work to earn £120?
W = hr
120 = h x 3
120 ÷ 3 = h
h = 40 hours
8B To solve each of the following, first write down a formula, and then substitute the given numbers and solve the equation.
1. Philip is paid £10 per hour and he works for 38 hours in a week. Find his weekly wage.
2. Richard is paid £7 per hour. How many hours must he work to earn £100?
3. Carpet cost £11 per square metre. How much will it cost to carpet a room measuring 5m by 4m?
4. Samantha wants to put a new carpet in her bedroom which has an area of 15m². She has £110. What is the price, in pounds per square metre, of the most expensive carpet that she can afford?