The price of a mango is 50 cents and the price of an orange is 45 cents. Shelia plans to make a batch of smoothies and so she buys 12 mangos and 24 oranges on Tuesday morning. When she checks the oranges on Wednesday, she fi nds 4 of them are rotten. Sheila returns to the shop and the shopkeeper agrees to refund the price of the 4 rotten oranges.
(i) Write an expression in words for the total cost of any number of mangos and any number of oranges. (ii) Write an algebraic expression for the cost (in cents) of any number of mangos and any number of oranges. (iii) Write an algebraic expression for the cost (in euros) of any number of mangos and any number of oranges. (iv) Find how much Sheila had to pay (in euros) for the mangos and oranges she bought on Tuesday. (v) Find the value (in cents) of the mangos and oranges Sheila had at the end of Wednesday.
Solution
(ii) (iii) (iv)
€1 = 100 cents
Practice questions 20.2
1. Evaluate the following if b = 2 (i) 2b (ii) 4b − b (iii) 10b − 6b
2. Evaluate the following if a = 3, b = − 1 and c = 5
(i) 2a + 3b (ii) ac + b (iii) b + 2c − a
__ 2
(iv) 3a − b
_____ c
(v) c(a − 3b) (vi) ca
3. Find the value of the following if b = − 4 (i) 2b
(ii) 8b− b (iii) b − 6b
__ 2
___ 8
(iv) b – 16b (v) − 5b (vi) − b
___ 4
4. Evaluate each of the following algebraic expressions when x = 4 and y = 2
(i) x + y (ii) x − y (iii) 5x − 2y
318 Linking Thinking 1
(iv) y − x (v) 3x2
− 5 (vi) 5y − 2y2 + 10
______ 4
____ 5 − 12
(iv) 21b – 12 b (v) 0b (vi) − b − b
5. Evaluate the following expressions when y = 6·5
(i) 5y + 1 (ii) 30 − 26 ÷ y
(iii) y2
6. Mary is saving for a violin. Mary’s aunt gives her €45 to start and Mary saves €3 each week.
(i) Write an expression in words for the amount Mary would save in w weeks.
(ii) Write an algebraic expression for the amount Mary would save in w weeks.
(iii) Evaluate how much Mary will save in 14 weeks.
(iv) Evaluate how much Mary will save in 20 weeks.
7. The area of a rectangle of length, l , and width, w , is given by the algebraic expression lw . Find the area of each of the following rectangles.
(i) Length = 6 cm and width = 5 cm (ii) Length = 12·2 m and width = 4·6 m