Page 61 - Math Smart - 7

Answer the following.
a) Find the odd one out when m = 7.
i) m + 5 ii) 21-m iii) 2m-2
b) Find the value of a that makes all of these expressions equal,
i) 2a + 1 ii) 10-a iii) 3a-2
c) Find the values of x and y that makes all of these expressions equal,
i) a: + 2_v + 16 ii) 2x + 2_v + 15 iii) x + 3_y + 11
o y = 4 z = 3
Write two expressions in y and s that have the value of
a) 16, b) 20, c) 19.
Is each pair of expressions equal? Use substitution to explain your
answer.
a) 3x and x + 3 b) x^and 2x c) 4x^and {4x)^

3.2.2 Working with formulae

We construct a formula to find the solution with a range of values to any word
problem. Choose the first letter of each quantity to represent the quantity before
expressing the rule in algebraic terms.

Example 2

O Adela is 8 years older than Olivia.
a) Write down an expression connecting Adela and Olivia's ages in words.
b) If Adele is A years old and Olivia is 0 years old, write a formula
connecting A and 0.
@ A book costs $12 and a magazine costs $8.
a) Work out the total cost of 5 books and 2 magazines.
b) Work out the total cost T in dollars of b books and m magazines.
O The formula for converting /itres to millilitres is to multiply the number of
litres by 1000.
a) Use the letters in red to write the formula using variables.
b) Use the formula to calculate the number of millilitres in 1.2 litres.

Solution
O a) Adela's age = Olivia's age + 8 years
8
b) A = 0 +
© a) Total cost = 5x$12 + 2x$8
= $60+ $16
= $76

b) T = bx 12+ mxB
T = 12b + 8m
O a) Number of millilitres = 1000 x number of litres
m = 1000 X /
b) m = 1000x 1.2
= 1200 millilitres
e