Hello. I need some help please with the below math problem.
The variables x and y are related proportionally. When x=6, y=16
Find y when x=45.
When x=45 y=
How would I go about solving this?
Please help
Proportional means y = k x where k is a constant
or
y2/x2 = y1/x1 = y5/x5 etc
so the first way
16 = k * 6
so k = 16/6 = 8/3
then
y = (8/3) 45
= 8 * 15 = 120
then the second way
16/6 = y/45
y = 45 * 16/6 = 45 * 8/3 oh well we have been there already
Hello Damon.
I am trying to understand something on the first way you just showed.
K=16/6 which is like a fraction and I see how you reduced it to 8/3
y=(8/3) 45
How did you get 8 x 15=120
How did you figure that out?
(8/3)45 = 8 * 45/3 = 8 * 15
Well I think you can multiply 8 * 15 but the way I actually did it in my head was :
8 * 15 = 8( 10 + 5) = 80 + 40 = 120
How do you get 8 x 15=120?
Hello Damon. The you are very smart. I am stuck on (8/3) 45
I don't get it still with the way you explained it. What do I need to do with the number 45?
8/3 is like a fraction and then 45? What am I multiplying together?
hey if all else fails use your calculator but here is a third way
8 = 2 * 2 * 2
so
8 * 15 = 2*2*2 * 15
= 2*2 * 30
= 2 * 60
= 120
Hello Damon.
I think I understand.
8/3=45/1
45 x 8=360
3 x 1=3
360/3=120
So is does y=120?
45 times 8 divided by 3
but 45 divided by 3 is 15
so we have
15 times 8
which is 120
remember a/b * c = a * c/b
(2/4)(4) = 2 (4/4) = 2
distributive property see:
https://www.mathsisfun.com/definitions/distributive-law.html
That makes a bit more sense. So but y=120 right?
y=mx+b is the formula for a line (google it), substitute (8/3) for m and 0 for b. Then use the equation y=(8/3)x for any value.
Test: 16 = (8/3) * 6
for x = 45
y=(8/3) * 45 = 120
I think I understand.
your way
8/3=x/45 multiply both sides by 3
8 = 3 x / 45 multiply both sides by 45
8 * 45 = 3 x divide both sides by 3
8 * 15 = x
120 = x
That is the way I showed him first Matt with b = 0
y = k x
Learn these rules :
https://www.mathsisfun.com/associative-commutative-distributive.html
So Y/x is constant: when you double X, Y doubles; when you triple X, Y triples, and etc.
Y/X = 16/6 = Y/45.
16/6 = Y/45,
Multiply both sides by 45:
Y = 45(16/6) = 120.