Answer:
x = - 1
Step-by-step explanation:
Given
2 = 3x + 5 ( subtract 5 from both sides )
- 3 = 3x ( divide both sides by 3 )
- 1 = x
<span>In order to find the breakeven number of game rentals, we need to find the point at which the costs are equal. To do this, we set two expressions as a function of the number of games, equate them, and solve.
For Fun Guys, cost C = 20 + 6.5g, where g is the number of games
For Game Bank, C = 50 + 3.5g
Equating -> 20 + 6.5g = 50 + 3.5g -> 3g = 30 -> g = 10
At 10 games, the cost will be the same for both stores, and that cost is 50 + 3.5* 10 = 20 + 6.5*10 = $85.</span>
Let us say that:
a = ones
b = fives
c = twenties
So that the total money is:
1 * a + 5 * b + 20 * c = 229
=> a + 5b + 20c = 229 -->
eqtn 1
We are also given that:
c = a – 5 -->
eqtn 2
a + b + c = 30 -->
eqtn 3
Rewriting eqtn 3 in terms of b:
b = 30 – a – c
Plugging in eqtn 2 into this:
b = 30 – a – (a – 5)
b = 35 – 2a -->
eqtn 4
Plugging in eqtn 2 and 4 into eqtn 1:
a + 5(35 – 2a) + 20(a – 5) = 229
a + 175 – 10a + 20a – 100 = 229
11a = 154
a = 14
So,
b = 35 – 2a = 7
c = a – 5 = 9
Therefore there are 14 ones, 7 fives, and 9 twenties.
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