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2 years ago

Solve the absolute value inequality for y:

Mathematics

1 answer:

Aleksandr [31]2 years ago

4 0

How are ya today? Hope your doing good :) stay safe and wear your mask!

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Please answer ASAP and if you do you will get Brainliest. Catherine buys a gallon of ice cream from the store. After taking it h

rodikova [14]

Answer:

Catherine's sister ate 2/15 gallons of the ice cream.

$\displaystyle \frac{2}{15}$ .

Step-by-step explanation:

Let $x$ be the amount of ice cream that Catherine's sister ate, in gallons.

Original amount: 1 gallon.

What Catherine ate: $\displaystyle \frac{1}{5}$ gallons.
What Catherine's sister ate is assumed to be $x$ gallons.

What's left: $\displaystyle \frac{2}{3}$ gallons.

Consider the relationship:

$\text{Original amount - What Catherine ate - What Catherine's Sister ate}\\ =\text{ What's left.}$ .

That is:

$\displaystyle 1- \frac{1}{5} - x = \frac{2}{3}$ .

Add $x$ to both sides of this equation:

$\displaystyle 1 - \frac{1}{5} = \frac{2}{3} +x$

Substract $\displaystyle \frac{2}{3}$ from both sides:

$\displaystyle 1 - \frac{1}{5} - \frac{2}{3} = x$ .

Convert the denominator of all three numbers on the left-hand side to $3 \times 5 = 15$

$\displaystyle \frac{15}{15} - \frac{3}{15} - \frac{10}{15} = x$ .

$\displaystyle x = \frac{2}{15}$ .

In other words, Catherine's sister ate $\displaystyle \frac{2}{15}$ gallons of the ice cream.

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