Question

During Appreciation Day, a school bought some roses and cookies for their parents volunteers. The school spent a total of $228. The number of roses bought to the number of cookies bought was 5:3.
They paid $12 more for the roses than the cookies
Each cookie was $0.60 more than each rose.
a) How much did the school spend on roses?
b) How many cookies did the school buy?

Answer 1

The number of roses bought to the number of cookies bought was 5:3.
Let each cookies is $x *
each rose is $y.
According to the question x = y + 0.60
Let no. of roses = 5x
no. of cookies = 3x
Cost of 5x roses = 5y
Cost of 3x cookies = 3x * = 3x(y + 0.60)
They paid $12 more for the roses
5*y = 3x(y + 0.60) + 12
=> 2*y = 1.8x + 12 ———- (1)
The school spend total of $228.
Hence 5*y + 3x(y + 0.60) = 228
=> 8 * y + 1.8x = 228
=> 4 (1.8x + 12) + 1.84x = 228 (using (1))
=> 72x + 48 + 1.8x = 228
=> 9x = 228 - 48
=> 9x = 180
=> x = 180/9 = 20
No. of roses = 5 * 20 = 100
No. of cookies = 3 * 20 = 60

Now from (1) - 2 * y = 1.8x + 12
=> 40y = 36 + 12
=> y = 48/40 = 1.2
x = y + 0.50 = 1.2 + 0.60 = 1.8
(a) The school spend on the roses = 100 * 1.2 = $120
(b) The school buy 60 cookies