Q3. - Algebra 1

Question

An ice-cream should be stored at $5^{\circ }\text{F}$ with an allowance for $5^{\circ }$. Write and solve an equation to find the maximum and minimum temperature at which the ice-cream should be stored.

Step-by-Step Solution

Answer

The minimum temperature at which ice cream can be stored is $0^{\circ }\text{F}$.

The maximum temperature at which ice cream can be stored is ${10}^{\circ }\text{F}$.

Step-1. Given data and its interpretation.

Ice-cream should be stored at $5^{\circ }\text{F}$.

Temperature allowance is $5^{\circ }\text{F}$, that means, $5^{\circ }\text{F}$ more than $5^{\circ }\text{F}$ and $5^{\circ }\text{F}$ less than $5^{\circ }\text{F}$ is suitable for the ice cream

Step-2. Apply the concept of Variables and Constants.

Variables: - In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

Constants: - In any expression or equation, the constants are the values that are fixed.

While performing addition in an equation, the same kind of elements or like terms are added together.

Step-3. Concept of absolute value.

Absolute value: - Absolute value of any quantity simply means the positive value of that quantity.

Example: -

Consider a variable x. Here, x can be both positive or negative but $\left|x\right|$ will always be positive and hence the absolute value.

Step-4. Calculation.

Let the temperature at which ice cream can be kept be x. 

Therefore, the equation will be: $x=5°\mathrm{F}\pm 5°\mathrm{F}$.

Consider $x-5=\pm 5$.

Use the concept of absolute numbers for $x-5=\pm 5$. The equation will be:- $\left|x-5\right|=5$.

Case 1: - $x-5=5$

On solving $x-5=5$, the obtained value of x will be

$\begin{array}{l}x-5+5=5+5\\ x=10\end{array}$

Case 2: - $x-5=-5$

On solving $x-5=-5$, the obtained value of x will be

$\begin{array}{l}x-5+5=-5+5\\ x=0\end{array}$

Hence $x=0°\text{F}$ and $x=10°\text{F}$.

Hence, the ice cream can be stored between $\text{0}°\text{F}$ and $\text{10}°\text{F}$.

The minimum temperature to store ice-cream $\text{=0}°\text{F}$.

The maximum temperature to store ice-cream $\text{=10}°\text{F}$.