1. ## proportional reasoning

On the number line above, a and b represent distances between numbers as shown. If the ratio of a to b is 1 to 6, what is the value of b ?

2. Originally Posted by aeroflix
On the number line above, a and b represent distances between numbers as shown. If the ratio of a to b is 1 to 6, what is the value of b ?
1 is to six as k is to k^2.

Set up and solve.

3. 36?

4. Originally Posted by aeroflix
36?
Yes, that is k^2...k^2-k=b, right?

5. but according to here

SAT Skills Insight

check skill 8 exanple. the answer is 42. what the? their wrong

6. Originally Posted by aeroflix
but according to here

SAT Skills Insight

check skill 8 exanple. the answer is 42. what the? their wrong
42=k+k^2...so I would say that they are wrong, but I've been known to be wrong myself at times.

It's elementary

$\frac{1}{6}=\frac{k}{k^2}$
$\frac{1}{6}=\frac{1}{k}$
$k=6,k^2=36$...

Maybe Im not seeing things right.

7. yah , they say b is 42. and we say b is 36. did u check the website?

8. Originally Posted by aeroflix
On the number line above, a and b represent distances between numbers as shown. If the ratio of a to b is 1 to 6, what is the value of b ?
$\frac{a}{b} = \frac{k}{k^2-k}$

$\frac{1}{6} = \frac{1}{k-1}$

$k-1 = 6$

$k = 7$

$b = k^2 - k = 49 - 7$