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21) Total number of cups: 26
6) Solution of the equation: x = -12
7) Father's age: 40
4) Distance driven: 400 miles
Step-by-step explanation:
21)
Let's call:
the height of each cup
the total height available in the dispenser
We are told that each cup added to the stack add a height of
We can therefore solve the problem by writing the following equation:
which means that the total height available (H) is filled by the height of one cup (h) + the number of additional cup multiplied by 0.8.
Solving for N:
And including the first cup, the total number of cups is
6)
The equation that we have to solve is
We proceed as follows:
First of all, we add +1 on both sides of the equation,
Now we multiply by 2 on both sides:
And now we divide both sides by 5:
7)
Let's call:
k = Karma's age
f = father's age
We are told that Karma is 13 years old, so
k = 13
Also, Karma's age is 2 years less than 3/8 of the father's age, so we can write
By combining the two equations,
And solving for f, we find:
So, the father's age is 40.
4)
Let's call:
T = 16 the total volume of the tank (16 gallons)
We also know that the car burns 0.03 gallons per mile, so the amount of fuel consumed after x miles is
This means that the amount of fuel left after x miles is
We also know that the amount of fuel left is 4 gallons, therefore:
So, 400 miles.
Learn more about equations:
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