Question

The capacities (in L) of two oil-storage tanks are x and y. The tanks are initially full; 1400L is removed from them by taking 40% of the contents of the first tank and 10% of the contents of the second tank. (a) Express y as a function of x, (b) Find f(500).

I can do the math; I just need a little help setting up the equation(s)

Answer 1

Let's first let the capacity of the first tank be x and the capacity of the second tank be y.

Answer 2

Knowing this, we know that 1400L is equal to 40% of x and 10% of y, correct?

Answer 3

How would we express this as an equation?

Answer 4

1400L = .4x + .1y ?

Answer 5

Correct. If we want to express y as a function of x, then just isolate y.

Answer 6

14000L = 4x + y
y=14000L - 4x (?)

Answer 7

I multiplied by 10 to remove the decimals then isolated y. We still get the same answer in the end, yes?

Answer 8

Yes, that equation is correct. Do you know how to find f(500)?

Answer 9

not sure where in the equation it would be.

Answer 10

(a) Express y as a function of x
means do what you just did: y=14000L - 4x
you can rename "y" to f(x), and write it as
f(x) = 14000L - 4x

Answer 11

f(500) means that you're letting x = 500.

Answer 12

In other words, what you have to do is plug in 500 into the equation you got.

Answer 13

so f(x) =14000L - 4(500)
f(x) =14000L - 2000

Answer 14

Correct. f(500) = 12000L

Answer 15

yes, but the L stands for liters. the 2000 is also in liters

Answer 16

okay. wasn't sure if I should continue to simplify since the variable was not explicit

Answer 17

L isn't a variable, it's just the unit, and x was in the same units :)

Answer 18

sigh. I overthink things and make a simple question harder than it is. Thankee-sai to you both.