Step-by-step explanation:
A is directly proportional to B is written as
A = kB
where k is the constant of proportionality
First we must find the relationship between the two variables
when
A = 5/3
B = 5/6
Substitute the values into the formula to find k
[tex] \frac{5}{3} = k \frac{5}{6} [/tex]
Multiply through by the LCM which is 6
That's
[tex]5 \times 2 = 5k[/tex]
5k = 10
Divide both sides by 5
k = 2
So the formula for the variation is
A = 2B
when B = 1/3
[tex]A = 2 \times \frac{1}{3} [/tex]
[tex]A = \frac{2}{3} [/tex]
When A = 15/2
[tex] \frac{15}{2} = 2B[/tex]
Multiply through by 2
[tex]4B = 15[/tex]
Divide both sides by 4
[tex]B = \frac{15}{4} [/tex]
Hope this helps you
