Question

How would I write these problems?

Answer 1

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:

$h=10 cm$ the height of each cup

$H=30 cm$ the total height available in the dispenser

We are told that each cup added to the stack add a height of

$\Delta h = 0.8 cm$

We can therefore solve the problem by writing the following equation:

$H=h+N\Delta h$

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:

$N=\frac{H-h}{\Delta h}=\frac{30-10}{0.8}=25$

And including the first cup, the total number of cups is

$N+1=25+1=26$

6)

The equation that we have to solve is

$\frac{5}{2}x-1=-31$

We proceed as follows:

First of all, we add +1 on both sides of the equation,

$\frac{5}{2}x-1+1=-31+1\\\frac{5}{2}x=-30$

Now we multiply by 2 on both sides:

$\frac{5}{2}x\cdot 2=-30\cdot 2\\5x=-60$

And now we divide both sides by 5:

$\frac{5x}{5}=\frac{-60}{5}\\x=-12$

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

$k=\frac{3}{8}f-2$

By combining the two equations,

$13=\frac{3}{8}f-2$

And solving for f, we find:

$\frac{3}{8}f=13+2\\\frac{3}{8}f=15\\3f=15\cdot 8 =120\\f=\frac{120}{3}=40$

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

$0.03 x$

This means that the amount of fuel left after x miles is

$16-0.03x$

We also know that the amount of fuel left is 4 gallons, therefore:

$16-0.03x=4\\0.03x=16-4\\0.03x=12\\x=\frac{12}{0.03}=400$

So, 400 miles.

Learn more about equations:

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