Question

This year, the Start-of-Term feast had three desserts: chocolate eclairs, raspberry tarts, and jam doughnuts. On the dessert table, there were two doughnuts for every three eclairs, and six eclairs for every five tarts. How many tarts were on the dessert table if there were a total of 1320 desserts?

Answer 1

Let
x = chocolate eclairs
y = raspberry tarts
z = jam donuts
We write the following system of equations:
z = (2/3) x
x = (6/5) y
x + y + z = 1320
Solving for y:
z = (2/3) (6/5) y
z = (4/5) y
then
(6/5) y + y + (4/5) y = 1320
3y = 1320
y = 1230/3 = 410
answer
there were 410 tarts on the dessert table

Answer 2

Each unit of dessert consists of five tarts, six eclairs and four doughnuts (since there are two for every three eclairs, or four for six). Each unit is therefore 15 deserts. 1320 deserts is 88 units. Each unit has five tarts, so the number of tarts is 88 times 5, or 440.