Question 1205856
let the mass of the cup = y
your two equations that need to be solved simultaneously are:


y + .4x = 158.3
y + .6x = 189.5


subtract the first equation from the second to get:


.2x = 31.2


solve for x to get:


x = 31.2 / .2 = 156.


replace x in the first of the original equations to get:


y + .4 * 156 = 158.3
solve for y to get:
y = 158.3 - .4 * 156 = 95.9


that's the mass of the cup.


the mass of a full cup will be 95.9 + 156 = 251.9 grams.


the equation can be graphed.


here's what it looks like.


<img src = "http://theo.x10hosting.com/2024/012801.jpg">


the equation is in slope intercept form.
the y-intercept is 95.9 which is the weight of the cup without any mass in it.
the slope is 156 which is the number of grams of mass in a full cup.
the value of x goes from 0 to 1, representing the proportion of mass in the cup from the time it's empty to the time it's full.