In order for him to have a 77% on his first 5 tests, that means the total amount of points earned on those 5 tests was 385 points out of 500 points.
(77*5 out of 5*100 points)
So if we want to add a test and have a 80% average this is what we have to do:
(385+x)/6 = 80 (multiply by 6 on both sides)
385 + x = 480 (minus 385 on both sides)
x = 95
If it's refilled with 8 litres of mango juice, the resulting mixture will be 8 parts mango and 48 parts pine, or 1 part mango, 6 parts pine. (AKA, roughly 16.67% mango juice).
Now, if they take out 8 litres from that mixture, that 8 litres will also be 1 part mango and 6 parts pine, leaving you with 48 litres of 1 part mango, 6 parts pine.
Hang on, because it gets tricky from here. We're going to use a formula here:
<---- where there are q[1] litres of p[1] % that we start with, and we add q[2] litres of p[2] % mix, and so we'll end up with a mixture that is (q[1] + q[2]) liters big that will have a different percent mixture p[3] from what we started.
We started with 48 liters that is 16.67% mango. So <---- change the percent to a decimal.
We're going to add 8 liters of pure mango juice, so <--- The 100% mango juice is the 1 in decimal.
As total mix, we'll have litres which is 48 + 8 = 56, BUT the percentage mango of the new mixture will surely be different.
So our equation so far is: . All we have to do is solve for .
<---- simplified
<--- roughly 28.57% mango juice or mango juice. Since mango is 2/7 of the mixture, the other 5/7 is pine. The problem asked for the ratio between mango to pine, and that would be the 2:5.
The lines are
i) y=-x+6
ii) y=2x-3
The solution of the system of equations is found by equalizing the 2 equations:
-x+6=2x-3
-2x-x=-6-3
-3x=-9
x=-9/(-3)=3
substitute x=3 in either i) or ii):
i) y=-3+6=3
ii) y=2(3)-3=6-3=3
(the result is the same, so checking one is enough)
This means that the point (3, 3) is a point which is in both lines, so a solution to the system.
In graphs, this means that the lines intersect at (3, 3) ONLY
Answer: The graph where the lines intersect at (3, 3)
To write in slope-intercept form, you first need to get y by itself. To do this, subtract 7x from both sides of the equation.
Doing this gets you: y = 25 - 7x
Now that y is by itself, remember that slope-intercept form looks like this: y = mx + b
So, let's switch the right side.
y = -7x + 25
Slope intercept form is: y = -7x + 25
Rules for y in Slope-Intercept form:
y must be positive
y must be by itself (so, not 2y, or anything with it... just y)
Cost of Sugar per pound = 3.29$
Cost of sugar for 7.9 pounds =
=>3.29 x 7.9
=>25.991$
Rounded to nearest 100ths place = 26.000$
