Question

A supermarket sells tuna in 90 g and 200 g tins. In one day, 112 tins of tuna were sold, with a total mass of 18 kg. How many tins of each type were sold?

a) Number of 90g tins
b) Number of 200g tins
c) Total number of tins
d) Total mass of tuna sold

Answer 1

The number of 90g tins sold is 40 and the number of 200g tins sold is 72. The total number of tins sold is 112 and the total mass of tuna sold is 18 kg (18000 g).

Step-by-step explanation:

Let's assign variables to represent the number of 90g tins and 200g tins sold. Let's say x represents the number of 90g tins and y represents the number of 200g tins.

We can set up the following system of equations:

1. x + y = 112 (equation 1) - this represents the total number of tins sold
2. 90x + 200y = 18000 (equation 2) - this represents the total mass of the tuna sold in grams (18 kg = 18000 g)

To solve this system of equations, we can use the method of substitution or elimination:

1. Substitution Method:

From equation 1, we have x = 112 - y.

Substituting this value of x into equation 2:

90(112 - y) + 200y = 18000

Expand and simplify the equation:

10080 - 90y + 200y = 18000

Combine like terms:

110y = 7920

Divide both sides by 110:

y = 72

Substitute this value of y back into equation 1:

x + 72 = 112

Subtract 72 from both sides:

x = 40

So, a) the number of 90g tins sold is 40, b) the number of 200g tins sold is 72, c) the total number of tins sold is 112, and d) the total mass of tuna sold is 18 kg (18000 g).