Question

Two types of flour X and Y cost sh.60 and 72 per kilogram, respectively. They are mixed such that one kilogram of mixture costs sh.70. Work out the ratio in which they were mixed.

a) 2:1
b) 3:1
c) 1:2
d) 1:3

Answer 1

The flours X and Y are mixed in a ratio that achieves a total cost of sh.70 per kilogram for the mixture. By setting up an equation based on the costs and solving for the quantities of each type of flour, it is determined that the flours are mixed in a ratio of 1:5, which is not listed among the provided options.

Step-by-step explanation:

To solve the problem, we need to set up an equation that represents the mixing of flour X and Y to achieve a kilogram of mixture that costs sh.70. Let's denote the quantity of flour X as 'x' kilograms and the quantity of flour Y as 'y' kilograms. The price per kilogram of flour X is sh.60, and the price per kilogram of flour Y is sh.72.

The total cost of the x kilograms of flour X would be 60x, and the total cost of the y kilograms of flour Y would be 72y. Since the mixture weighs one kilogram in total, we have the equation x + y = 1. The total cost for the mixture is therefore 60x + 72y, and this must equal the total cost of the mixture, which is sh.70. Hence, the equation can be written as 60x + 72y = 70.

Using the x + y = 1 equation, we can find that y = 1 - x. We substitute y in the cost equation: 60x + 72(1 - x) = 70. Simplifying this equation we get 60x + 72 - 72x = 70, which results in -12x = -2, hence x = 1/6. Then y can be determined as y = 5/6.

So, x : y = 1/6 : 5/6. When we simplify this ratio by multiplying both terms by 6, we get 1 : 5. Therefore, flours X and Y are mixed in a ratio of 1:5, which is not one of the provided options.