SOLUTION: Hi When a cup is 40% full it has a mass of 158.3g. When it is 60% full it has a mass of 189.5g. What is the mass When it is 100% full.

Question 1205856: Hi
When a cup is 40% full it has a mass of 158.3g. When it is 60% full it has a mass of 189.5g. What is the mass When it is 100% full.
Found 4 solutions by math_tutor2020, Theo, josgarithmetic, greenestamps:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

c = mass of the empty cup, or just the mass of the cup itself ignoring the contents
w = mass of the water (or whichever liquid) inside when 100% full, ignoring the mass of the cup

c+0.40w = is the mass when the cup is 40% full
c+0.40w = 158.3
solving for c gets us
c = 158.3-0.40w

c+0.60w = is the mass when the cup is 60% full
c+0.60w = 189.5

Let's plug c = 158.3-0.40w into the other equation
c+0.60w = 189.5
158.3-0.40w+0.60w = 189.5
158.3+0.20w = 189.5
I'll let the student take over from here.
Solve that equation to find w.
Hint: The value of w is between 140 and 160.

After determining the value for w, use it to find c.
The last step is to compute c+w to get your final answer.
c+w = mass of the cup when 100% full

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
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.

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.

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Three linear points:
(40,158.3), (60,189.5), (100,y)

slope (189.5-158.3)/20
slope is 1.56

Using point-slope form

---------here, in slope-intercept form

Question asks what is y if x is 100.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

The numbers are "nice", making it easy to solve this problem informally.

From 40% full to 60% full is an increase of 20%, corresponding to an increase in mass of 189.5-158.3 = 31.2g.

From 60% full to 100% full is a change of 40%, which is exactly twice the change from 40% to 60%; so the change in mass will be twice the change from 40% to 60%.

2*31.2g = 62.4g; the mass when the cup is 100% full will be 189.5+62.4 = 251.9g.

ANSWER: 251.9g

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