Math Problem?

Question

How Tall Are The Flowers?
Jennie and Trevor measured the heights of two beautiful flowers growing in a garden – one red
and one blue.
(a) Jennie told her friend Sara that five times the height of the blue flower added to four times
the height of the red flower is exactly one metre. Show all the possible heights of the flowers.
(b) From Jennie’s information, Sara didn’t know the actual heights of the flowers, so she asked
Trevor what he had found out. He told her that the red flower is seven centimetres taller than
the blue one. show the possible heights of the two flowers based on this information.

Answer 1

(a)1meter = 5b +4r

(b)Using r = b+7;

1meter = 5b + 4(b+7)
1 meter = 5b +4b +28
1 meter = 9b +28cm
9b = 100cm - 28cm
b = 8cm; Blue flowers are 8cm tall/high
100 = 5*8 +4*r
60 = 4*r
r = 15cm
red flowers are 15cm tall/high

Answer 2

a)
Let x = ht of blue flower
Let y = ht of red flower
5x + 4y = 100cm
That line gives the heights where x>0 and y>0 (the flowers exist and do not have negative height)

b)
y = x + 7cm
5x + 4(x + 7) = 100
9x + 28 = 100
9x = 72
x = 8cm
y = 15cm

check
8*5 + 4* 15 = 100
40 + 60 = 100
checks

Answer 3

the tall girl is hot