Question

Math SSAT Question

The height of a maple tree and a cherry tree have a ratio of 5:2. If the maple tree grew 20cm and 20cm was cut off of the top of the cherry tree, the ratio of their heights would be 3:1. How much taller is the maple tree than the cherry tree.

A. 240cm
B. 160cm
C. 400cm
D. 280cm
E. 260cm

Answer 1

@mathslover @Mertsj

Answer 2

Please explain the answer :)

Answer 3

when we say "the height of a maple tree and a cherry tree have a ratio of 5:2" we mean that: $$M=\frac52C$$when we read "the maple tree grew 20cm and 20cm was cut off of the top of the cherry tree, the ratio of their heights would be 3:1", that means that the ratio between the new maple tree height \(M+20\) and the new cherry tree height \(C-20\) is 3:1 i.e. $$M+20=\frac31(C-20)$$

Answer 4

now that we have a system of equations, you can use typical methods -- elimination, substitution, etc. -- to solve the system:

$$M+20=3(C-20)\\\frac52C+20=3C-60\\20=\frac12C-60\\80=\frac12C\\C=160$$

Answer 5

i.e. the cherry tree is 160 cm tall. can you find the height of the maple tree now?

Answer 6

The maple tree is 400cm and it is 240cm taller than the cherry tree

Answer 7

very good :-)

Answer 8

@oldrin.bataku Why would you put the ratio times the cherry tree instead of the maple. What is the rational? Im talking about the M= 5/2C part.

Answer 9

the rational \(5/2\) corresponds to the ratio \(5:2\); when we say the ratio of A to B is 1/2, for example, we mean \(A=\frac12B\)

Answer 10

in our case it is stated that the ratio is of the height of a maple tree *to* that of a cherry tree -- note the order of maple, cherry. this is our hint that we write \(M=\frac52C\)