There are 144 flowers. For every 9 roses, there are 15 tulips. How many of each flower is there? Solve with equation

Answer 1

If we denote by x the number of roses and y the number of tulips and assuming there is nothing other than roses and tulips, then we must have that

x + y = 144

that means that the sum of number of roses and the number of tulips should be the total number of flowers

Also we must have

y/x = 15/9 (or 15x = 9y)

because for every 9 roses we have 15 tulips

We then get two equations in two unknowns

x+y=144 (1)

15x=9y (2)

Expressing the second as y = (15/9)x and replacing it in equation (1) we get

x + (15/9)x = 144

that is

(24/9)x = 144

or

x =(144)/(24/9) = 54

Replacing this value of x in (1) we get 54 + y =144 or y = 144-54 = 90

This means that

x = 54

y = 90

So we have 54 roses and 90 tulips