Question

Joe and Ann buy some fruit from the same shop. Joe buys 4 apples and 3 bananas for £2.50 Ann buys 3 apples and 4 bananas for £2.40 Work out the cost of

(i) one apple
(ii) one banana​

Answer 1

apple costs $0.40 , banana costs $0.30

Explanation:

let a represent apples and b represent bananas , then

4a + 3b = 2.5 → (1)

3a + 4b = 2.4 → (2)

multiplying (1) by 4 and (2) by - 3 and adding will eliminate b

16a + 12b = 10 → (3)

- 9a - 12b = - 7.2 → (4)

add (3) and (4) term by term to eliminate b

7a + 0 = 2.8

7a = 2.8 ( divide both sides by 7 )

a = 0.4

substitute a = 0.4 into either of the 2 equations and solve for b

substituting into (1)

4(0.4) + 3b = 2.5

1.6 + 3b = 2.5 ( subtract 1.6 from both sides )

3b = 0.9 ( divide both sides by 3 )

b = 0.3

(i) one apple cost $0.40

(ii) one banana costs $0.30

Answer 2

(i) One apple = $0.40

(ii) One banana = $0.30

Explanation:

Given information:

• Cost of 4 apples and 3 bananas = £2.50
• Cost of 3 apples and 4 bananas = £2.40

Define the variables:

• Let x = The cost of one apple.
• Let y = The cost of one banana.

Create two equations with the given information and defined variables:

`\textsf{Equation 1}: \quad 4x+3y=2.50`

`\textsf{Equation 2}: \quad 3x+4y=2.40`

Multiply the first equation by 4:

`\implies 4 \cdot 4x+4 \cdot 3y=4 \cdot 2.50`

`\implies 16x+12y=10.00`

Multiply the second equation by 3:

`\implies 3 \cdot 3x + 3 \cdot 4y = 3 \cdot 2.40`

`\implies 9x + 12y = 7.20`

Subtract the equations to eliminate the term in y:

`\begin{array}{crcccc}& 16x & + & 12y & = & 10.00\\-& (9x & + & 12y & = & 7.20)\\\cline{2-6} & 7x & & &=&2.80\\\end{array}`

Solve for x:

`\implies 7x=2.80`

`\implies (7x)/(7)=(2.80)/(7)`

`\implies x=0.40`

Therefore, the cost of one apple is $0.40.

Substitute the found value of x into one of the equations and solve for y:

`\implies 4x+3y=2.50`

`\implies 4(0.40)+3y=2.50`

`\implies 1.60+3y=2.50`

`\implies 1.60+3y-1.60=2.50-1.60`

`\implies 3y=0.90`

`\implies (3y)/(3)=(0.90)/(3)`

`\implies y=0.30`

Therefore, the cost of one banana is $0.30.