The ratio of the price of a pen to the price of a ruler is 4:3. If the price of a ruler increases by 70p, then the ratio becomes 4:5.
Complete these sentences.
(a) The price of a pen is £
(b) The price of a ruler before the increase is £

(a) The price of the pen is $1.4

(b) The price of the ruler before the increase is $1.05

Step-by-step explanation:

∵ The ratio of the price of a pen to the price of a ruler is 4: 3

→ Multiply each term of the ratio by m, where m is a constant

∴ The cost of the pen = 4m

∴ The cost of the ruler = 3m

∵ The price of a ruler increases by 70p

→ Change 70 p to dollars by divide it by 100

∴ The price of a ruler increases by $0.7

∵ The old price of the ruler = 3m

∴ The new price of the ruler = 3m + 0.7

∵ The ratio between the pen and the ruler becomes 4: 5

∴ The price of the pen/the new price of the ruler =  

∴ The new ratio of the prices =

→ Equate the fraction of the ratio by the fraction of the prices

∴ =

→ By using cross multiplication

∵ 5 × (4m) = 4 × (3m + 0.7)

∴ 20m = 4(3m) + 4(0.7)

∴ 20m = 12m + 2.8

→ Subtract 12 m from both sides

∴ 8m = 2.8

→ Divide both sides by 8 to find m

∴ m = 0.35

(a)

∵ The price of the pen = 4m

∵ m = 0.35

∴ The price of the pen = 4(0.35)

∴ The price of the pen = $1.4

(b)

∵ The price of the ruler before the increase = 3m

∵ m = 0.35

∴ The price of the ruler before the increase = 3(0.35)

∴ The price of the ruler before the increase = $1.05