(a) Alex, Bobbie and Chris share strawberries in the ratio
Alex : Bobbie : Chris = 3 : 2 : 2
Chris receives 12 strawberries. Calculate the total number of strawberries shared.
(b) In a sale, a shop reduces all prices by 12%.
(i) Dina buys a book which has an original price of $6.50.
Calculate how much Dina pays for the book.
(ii) Elu pays $11 for a toy.
Calculate the original price of the toy.
(c) Feri invests some money.
The rate of interest for the first year is 2.5%.
At the end of the second year the overall percentage increase of Feri’s investment is 6.6%.
Find the rate of interest for the second year.
(d) A radioactive substance decays at an exponential rate of 2% per day.
The initial mass is 80 g.
(i) Find the mass at the end of 5 days.
(ii) Find how many more whole days, after day 5, it takes for the mass to reduce to less than 67 g.
▶️ Answer/Explanation
(a) 42
Chris’s share is 2 parts = 12 strawberries, so 1 part = 6. Total parts = 3+2+2 = 7. Total strawberries = 7 × 6 = 42.
(b)(i) $5.72
Reduced price = Original price × (100% – 12%) = $6.50 × 0.88 = $5.72.
(b)(ii) $12.50
Let original price be x. Then x × 0.88 = $11 → x = $11 ÷ 0.88 = $12.50.
(c) 4%
After first year: 100 × 1.025 = 102.5. Overall after 2 years: 100 × 1.066 = 106.6. Second year interest = (106.6 ÷ 102.5 – 1) × 100 = 4%.
(d)(i) 72.3 g
Mass = Initial × (decay rate)^days = 80 × (0.98)^5 ≈ 80 × 0.9039 ≈ 72.31 g.
(d)(ii) 4 days
After 5 days: 72.3 g. We need to find n where 72.3 × (0.98)^n < 67. Trying n=4: 72.3 × (0.98)^4 ≈ 66.8 g which is less than 67 g.
(a) Tomas sells a computer, a bike, and a phone. The amounts he receives are in the ratio computer : bike : phone = 14 : 17 : 9.
(i) Calculate the amount he receives for the phone as a percentage of the total.
(ii) The total amount he receives is $560. Calculate how much he receives for the bike.
(iii) Tomas originally bought the bike for $195. He wanted to make a profit of at least 25% when he sold it. Does Tomas make a profit of at least 25%? Show all your working.
(b) Ulla invests $725 for 6 years in an account paying simple interest at a rate of 1.3% per year. Calculate the total interest earned at the end of 6 years.
(c) In a sale, all prices are reduced by 24%. Victor pays $36.86 for a pair of shoes in the sale. Calculate the original price of the shoes.
▶️ Answer/Explanation
(a)(i) 22.5%
Phone ratio is 9 parts out of total 40 parts (14+17+9). Percentage = (9/40) × 100 = 22.5%.
(a)(ii) $238
Bike ratio is 17 parts. Value per part = $560 ÷ 40 = $14. Bike amount = 17 × $14 = $238.
(a)(iii) No
25% profit on $195 would be $243.75. Tomas sold for $238 which is less than $243.75.
(b) $56.55
Simple interest = Principal × Rate × Time = $725 × 0.013 × 6 = $56.55.
(c) $48.50
Sale price is 76% of original (100%-24%). Original price = $36.86 ÷ 0.76 = $48.50.