Gael Woodward

Answered

2023-01-01

A motel clerk counts his $1 and$10 bills at the end of the day. He finds that he has a total of 48 bills having a combined monetary value of $138. How to find the number of bills of each denomination that he has? Answer & Explanation bagosiwp2 Expert 2023-01-02Added 16 answers First: Let's call the number of$1 bills: s
Let's call the number of $10 bills: t Using the data in the problem, we can then create the following two equations: Given that we know the motel clerk has a total of 48 bills: Equation 1: $$\displaystyle{s}+{t}={48}$$ We also know the 48 bills add up to$138, then:
Equation 2: $$\displaystyle\{1}{s}+\{10}{t}=\{138}$$
Step 1) The first equation for s must be solved:
$$\displaystyle{s}+{t}-{\color{red}{{t}}}={48}-{\color{red}{{t}}}$$
$$\displaystyle{s}+{0}={48}-{t}$$
$$\displaystyle{s}={48}-{t}$$
Step 2) In the second equation, swap out (48-t) for s, and then solve for t:
$$\displaystyle\{1}{s}+\{10}{t}=\{138}$$ becomes:
$$\displaystyle\{1}{\left({48}-{t}\right)}+\{10}{t}=\{138}$$
$$\displaystyle{\left(\{1}\cdot{48}\right)}-{\left(\{1}\cdot{t}\right)}+\{10}{t}=\{138}$$
$$\displaystyle\{48}-\{1}{t}+\{10}{t}=\{138}$$
$$\displaystyle\{48}+{\left(-\{1}+\{10}\right)}{t}=\{138}$$
$$\displaystyle\{48}+\{9}{t}=\{138}$$
$$\displaystyle\{48}-{\color{red}{\{48}}}+\{9}{t}=\{138}-{\color{red}{\{48}}}$$
$$\displaystyle{0}+\{9}{t}=\{90}$$
$$\displaystyle\{9}{t}=\{90}$$
$$\displaystyle\frac{{\{9}{t}}}{{\color{red}{\{9}}}}=\frac{{\{90}}}{{\color{red}{\{9}}}}$$
$$\displaystyle\frac{{{\color{red}{\cancel{{{\color{black}{\{9}}}}}}}{t}}}{\cancel{{{\color{red}{\{9}}}}}}=\frac{{{\color{red}{\cancel{{{\color{black}{\}}}}}}{\color{red}{\cancel{{{\color{black}{{90}}}}}}}{10}}}{{\color{red}{{\color{black}{\cancel{{{\color{red}{\}}}}}}{\color{black}{\cancel{{{\color{red}{{9}}}}}}}}}}$$
$$\displaystyle{t}={10}$$
Step 3) Substitute 10 for t in the solution to the first equation at the end of Step 1 and calculate s:
$$\displaystyle{s}={48}-{t}$$ becomes:
$$\displaystyle{s}={48}-{10}$$
$$\displaystyle{s}={38}$$
The motel clerk had 38 $1 bills and 10$10 bills.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?