You and some friends have $30. You want to order large pizzas (p) that are $9 each and drinks

1 answer:

6 0

Given:
Budget = $30
cost of pizza = $9
cost of drinks = $1
number of pizza = p
number of drinks = d

pizza and drinks should only be equal to or less than the budget of $30.

$9p + $1d < $30

unit cost of pizza : 9
unit cost of drinks : 1
total cost of set (p & d) 10

pizza = 9/10 x 30 = 27 total cost of pizza
drinks =1/10 x 30 = 3 total cost of drinks

27 ÷ 9 = 3 number of pizzas to order
3 ÷ 1 = 3 number of drinks to order

To check:

9p + 1d < 30
9(3) + 1(3) < 30
27 + 3 < 30
30 < 30

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Additional comment

When faced with a system of linear equations, the first step is to look at them and observe where the variable terms are, and any relationships between coefficients. Several options are generally open to you for solving the equations. Methods generally taught first are ...

substitution
elimination

Substitution is handy when one of the variables or variable terms can be written (easily) in terms of the other variable. Elimination is handy when some simple multiple of one of the equations can be added to the other equation to cancel one of the variable terms (eliminate it).

Other available methods include matrix methods, Cramer's rule, and graphing. Working knowledge of all of these methods will help you identify the one that will be easiest to use in any given situation.

The availability of calculators able to use these methods greatly simplifies the task of finding a solution. It is simply a matter of entering the equations in the appropriate form.

One of my favorites is the graphing calculator, which only requires you type in the given equations and click on the solution point to find its coordinates.