Question

Andrew goes to the shop to buy some apples and bananas.

He goes to purchase 5 apples and 4 bananas, and the total comes to $ 5.70.

Unfortunality, he doesn’t have enough money, so he puts back 1 apple and 2

bananas.

The new total is $ 3.60. What is the cost of 1 apple and the cost of 1 banana?

b. Andrea’s budget is $6. If she buys equal number of apples and bananas, then

what is the maximum number of apples and bananas, she can buy?

Answer 1

a. The price of an apple is $0.5 and that of a banana is $0.8

b. 4

Explanation:

Form simultaneous equations from the information.

For 5 apples and 4 bananas, and the total comes to $ 5.70 this can be;

5 a + 4 b = $5.70----------i

After he puts back 1 apple and 2 bananas, the equation will be;

4 a + 2 b = $3.60 -------------ii

Solve the two equations simultaneously as;

{5 a + 4 b = 5.70 }4 ---------making the a terms equal to eliminate them

{4 a + 2 b = 3.60}5

20 a + 16 b = 22.80 -------subtract the b terms

20 a + 10b = 18.00

6 b = 4.80

b= 4.80/ 6

b=$ 0.8

Using equation i :

5a + 4b =$5.70

5a + 4*0.8 = 5.70

5a + 3.2 = 5.70

5a = 2.5

a = 2.5 / 5

a=$0.5

The price of an apple is $0.5 and that of a banana is $0.8

b.

Let the number of apples be ------x

Let the number of bananas be-----x

This is because the target is equal numbers;

Form an equation for total cost as;

0.5 x + 0.8 x = $6

1.3 x = 6

x = 1.3 / 6 = 4.62

Maximum number of bananas to buy = 4

Maximum number of apples to buy = 4

However, he will have $0.8 remaining