Question 85·Easy·Linear Equations in Two Variables
At a café, the total cost (in dollars) of buying muffins and drinks is given by the equation
If Sam spent $50 and bought muffins, how many drinks did he buy?
(Express the answer as an integer)
For linear word problems like this, first identify what each variable represents and what is being asked. Substitute all known values into the given equation so that only one variable is unknown. Then solve the resulting one-variable linear equation step by step: simplify, isolate the term with the variable, and divide by its coefficient. Keep track of units (dollars, items) to avoid confusing total money with number of items.
Hints
Plug in what you know
You know the total cost and how many muffins Sam bought. Replace and in the equation with those numbers.
Simplify the muffin part first
After you substitute , multiply and to find the total cost of the muffins.
Isolate the drinks term
Once you have something like , what operation should you do first to get by itself? After that, what do you do to solve for ?
Desmos Guide
Enter the equation with the known values
In Desmos, type 50 = 4*8 + 3x. Here, x represents the number of drinks.
Solve for the drinks variable
Either:
- Click on the left side of the equation and let Desmos solve for
x, or - Rewrite as
y = 4*8 + 3xandy = 50, graph both, and find the x-coordinate of their intersection.
The value of x that makes the equation true is the number of drinks Sam bought.
Step-by-step Explanation
Substitute the known values into the equation
We are told the total cost is $50 and Sam bought 8 muffins. The cost equation is
Substitute and :
Simplify and isolate the drinks term
First calculate :
So the equation becomes
Now subtract from both sides to get the term with alone on one side:
which simplifies to
Solve for the number of drinks
Now divide both sides of by to solve for :
So , meaning Sam bought 6 drinks.