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Answer:
Let's define the cost of the cheaper game as X, and the cost of the pricer game as Y.
The total cost of both games is:
X + Y
We know that both games cost just above AED 80
Then:
X + Y > AED 80
From this, we want to prove that at least one of the games costed more than AED 40.
Now let's play with the possible prices of X, there are two possible cases:
X is larger than AED 40
X is equal to or smaller than AED 40.
If X is more than AED 40, then we have a game that costed more than AED 40.
If X is less than or equal to AED 40, then:
X ≥ AED 40
Now let's take the maximum value of X in this scenario, this is:
X = AED 40
Replacing this in the first inequality, we get:
X + Y > AED 80
Replacing the value of X we get:
AED 40 + Y > AED 80
Y > AED 80 - AED 40
Y > AED 40
So when X is equal or smaller than AED 40, the value of Y is larger than AED 40.
So we proven that in all the possible cases, at least one of the two games costs more than AED 40.
Answer:
- One proportion to solve is 8/18 = x/8
- Exact answer as a fraction: x = 32/9
- Approximate answer in decimal form: x = 3.556
In reality, the 5's go on forever, but we have to round off somewhere.
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Explanation:
Break up the triangles as your teacher recommends. See the diagram below as to what I mean.
The smaller triangle has A = 8 as the horizontal side, and B = x as the vertical side
The larger triangle has C = 10+8 = 18 as the horizontal aside, and D = 8 as the vertical side.
We can form the proportion A/C = B/D.
A/C connects the horizontal sides (small/large) while B/D has the vertical sides tied together. The order of division is the same small over large. You could do large over small, but make sure you keep both sides consistent.
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Let's solve for x
A/C = B/D
8/18 = x/8
8*8 = 18*x .... cross multiply
64 = 18x
18x = 64
x = 64/18 .... divide both sides by 18
x = 32/9 exactly in fraction form
x = 3.556 approximately in decimal form
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Another proportion you can solve is A/B = C/D and you should get the same x value. It's the same as A/C = B/D because the B and C swap places. There are many other approaches you could take using different proportions.
When the function goes 1 to the right, it goes 2 down. Therefore the direction of the function is

Hence, the function represented is
y = -2x