Ben has 1 and a half times as many toy cars as Amanda. Clive has 3/4 as many cars as Ben. Clive has how many times many cars as Amanda?

Question

Ben has 1 and 1/2 times as many cars as Amanda. Clive has 3/4 as many cars as Ben. Clive has how many times many cars as Amanda? Who has more cars, Clive or Amanda? 

Answer 1

A: number of toy cars Amanda has

B: number of toy cars Ben has

C: number of toy cars Clive has

x: an unknown number

 

B=1.5A

C=0.75B

 

Question 1. C=Ax?

Question 2. C>A or A>C?

 

0.75B=0.75(1.5A)

0.75B=1.125A=C

1.125A=Ax

x=1.125

A=B/1.5=0.67B

 

Answer 1. C=0.75B

Answer 2. C>A

 

 

Answer 2

This is a subtitution/ratio question.  Setting the quantity of cars for Amanda (A), Ben (B), and Clive (C):

B=(3/2)A; (note that 1 and a half = 1.5 = 3/2)

C=(3/4)B;

 

We can relate Clive's car collection to Amanda's by solving for Ben's number of cars.  You can do so in either equation, but I'll choose the first...

 

Replacing B in the second equation with (3/2)A:

C = (3/4)((3/2)A);

C = (3/4)*(3/2)*A;

C = (9/8)*A;  We have now directly related Clive's and Amanda's cars collections.

 

Set to a mixed number (9/8) becomes 1 and one ninth.  Thus Clive has 1 and one ninth times as many cars as Amanda.  We would have gotten the same solution by substituting the other way, but there would have been more intermediate math steps.

 

To answer the second part of the question, we see that:

C = (9/8)*A;  Rearranging into a ratio we get:

C/A = 9/8;  This says that for every 9 cars that Clive has, Amanda has only 8 cars.

 

Thus, Clive has more cars in his collection than Amanda.