Problem Solving

If the ration of X to Y is 3 to 2, and the ratio of Y to Z is 5 to 4, then ratio of X to Z is

a) 15/6
b)15/8
c)4/5
d)8/15
e)1/2

chimwemwe wrote:If the ration of X to Y is 3 to 2, and the ratio of Y to Z is 5 to 4, then ratio of X to Z is

a) 15/6
b)15/8
c)4/5
d)8/15
e)1/2

Hi,

there are a number of ways to solve this, including picking numbers and various algebraic approaches. Let's start with one algebraic approach.

x/y = 3/2
y/z = 5/4

Since we want x/z, we need to make y "disappear". To do so, we can simply multiply the left sides of each equation together as well as the right sides:

(x/y)*(y/z) = (3/2)*(5/4)

xy/yz = 3*5/2*4

x/z = 15/8... choose (b).

If we wanted to pick numbers, we'd start with a value for y, since that's the variable we want to get rid of.

Looking at the two ratios, the first has y=2 and the second has y=5. In order to make the math work out nicely, let's let y equal the smallest common multiple of 2 and 5, 10.

So, if y=10, then:

x/10 = 3/2

x = 30/2 = 15

10/z = 5/4

40 = 5z

8 = z

Accordingly,

x/z = 15/8.