Question 136·Easy·Linear Equations in Two Variables
At a farmers market, apples cost $5 each and oranges cost $2 each. Luna buys a total of apples and some oranges for $26 in all.
If represents the number of apples and represents the number of oranges, the relationship can be modeled by the equation
If Luna bought apples, how many oranges did she buy?
For linear word problems like this, first translate the situation into an equation, then plug in any given values and solve for the unknown. Here, once you know the total cost and the cost and number of apples, substitute the known value, simplify to find how much money is left, and divide by the price per orange to get . On the SAT, this direct algebraic approach is usually faster and more reliable than guessing from the answer choices.
Hints
Use the equation you are given
Start with the equation and remember that is the number of apples and is the number of oranges.
Plug in the known value
You know Luna bought 4 apples. Replace with 4 in the equation and simplify the left-hand side.
Solve for step by step
After substituting , move the constant term to the other side to isolate , then divide by 2 to find .
Desmos Guide
Compute the value of directly
In Desmos, type the expression (26 - 5*4)/2 into an empty expression line. The value that Desmos outputs is the value of , which tells you how many oranges Luna bought.
Step-by-step Explanation
Substitute the given number of apples
We are told Luna bought 4 apples, so .
Substitute this into the equation:
Isolate the orange term
First calculate the cost of the apples:
So the equation becomes
Subtract 20 from both sides to get the term with alone on one side:
Solve for the number of oranges
Now divide both sides of by 2:
So Luna bought 3 oranges.