Question

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QUESTION 1

A fruit basket has both mangoes and oranges and can accommodate only 80 mangoes and oranges when

full. If there are x mangoes in a full basket,


(i) Write an expression for the number of oranges in it.


(ii) If an orange costs 50 cents and a mango costs 40 cents, write an expression for the amount of

money collected (in dollars) for the sale of all the mangoes and oranges in the full basket, S ( x ) .


(iii) Find the total amount collected from selling all the fruits in the full basket if there are 35 mangoes

in it.

​

Answer 1

(i)
`80-x`

(ii)
`S(x) = 40 - 0.10x`

(iii) $36.5

Explanation:

Given that:

1. Total Number of fruits = 80

2. Number of mangoes = x

3. Both mangoes and oranges are there in the basket.

Solution (i):

Only mangoes and oranges are there in the basket and the basket is full.

so, Number of mangoes + Number of oranges = Total number of fruits

x + Number of oranges = 80

Number of oranges =
`80 -x`

Solution (ii):

Given:

Cost of an orange = 50 cents = $0.50

Cost of a mango = 40 cents = $0.40

Cost for x mangoes =
`\$ 0.40x`

Cost for (
`80-x`) oranges =
`\$ 0.50 * (80-x)`

`\Rightarrow S(x) = 0.50 (80-x) + 0.40x\\\Rightarrow S(x) = 40 -0.50x + 0.40x\\\Rightarrow S(x) = 40 - 0.10x`

Solution (iii):

Put value of x = 35 in S(x)

`S(35) = 40 - 0.10 (35)\\\Rightarrow S(35) = 40 - 0.35\\\Rightarrow S(35) =\$ 36.5`

Hence, answers are:

(i)
`80-x`

(ii)
`S(x) = 40 - 0.10x`

(iii) $36.5