Question

Paul and four of his staff decide to go to lunch to discuss the new project. Between them they order 8 drinks, and 6 lunch specials. Paul pays for all the drinks. They split the cost for the lunch specials and a $37 tip. Write an algebraic expression that represents the amount that Paul has to pay if a drink costs d dollars and a lunch special is on sale for m dollars.Simplify the expression completely.List the terms in your expression.For each term, identify the coefficient and variable.

Answer 1

Step 1

Given;

$\begin{gathered} Paul\text{ and 4 of his staff went for lunch} \\ Paul\text{ paid for all drinks} \\ They\text{ order 8 drinks and 6 lunch special with a \ 37 tip} \\ Each\text{ drink cost \ d } \\ Lunch\text{ special \ m} \end{gathered}$

Step 2

Total amount spent on drinks

$\text{ \ }8d$

Total amount spent on lunch specials

$\text{ \ 6m}$

The total amount spent by 5 of them will be;

$\text{ \ 8d+\ 6m+\ 37}$

If the bill was split between them but paul paid for all the drinks. Paul wil pay;

$\begin{gathered} \text{ \ \lparen8d+}\frac{6m+37}{5}) \\ =\operatorname{\ }\operatorname{\lparen}\text{8d+}\frac{6m}{5}+\frac{37}{5})=\text{ \ \lparen8d+1.20m+7.40\rparen} \end{gathered}$

An algebraic expression that represents the amount that Paul has to pay

is;

$\text{ \ \lparen}8d+1.20m+7.40)$

The terms of the expression are;

$\begin{gathered} 8d,1.20m\text{ and 7.40} \\ For\text{ 8d-\lparen coefficient=8, variable=d\rparen} \\ For\text{ 1.20m-\lparen coefficient=1.20, variable=m\rparen} \\ For\text{ 7.40-\lparen it is a constant\rparen} \end{gathered}$