A restaurant sells pasta, pizzas and sandwiches. The ratio of plates of pasta sold to pizzas sold on Monday is 5:9, and the ratio of the number of pizzas sold to sandwiches sold is 3:2.

(a) What is the ratio of the number of plates of pasta to pizzas to sandwiches sold?

(b) If 120 sandwiches were sold, how many plates of pasta and how many pizzas were sold?

Pasta:

Pizzas:

(a) The ratio of the number of plates of pasta to the number of pizzas sold is 5:9.

The ratio of the number of pizzas to sandwiches sold is

3:2 = (3 × 3) : (2 × 3) = 9:6

Thus, the ratio of plates of pasta to pizzas to sandwiches sold is 5:9:6.

(b)

Use the method of finding an equivalent ratio to find the number of the other two parts.

We can make a chart.

Pasta : Pizzas : Sandwiches

5 : 9 : 6

5 × a : 9 × a : (6 × a = 120)

From the chart above we know that, a = 120 ÷ 6 = 20

Thus,

Pasta: 5 × 20 = 100

Pizzas: 9 × 20 = 180