Question 44·Medium·Linear Equations in Two Variables
At a farmers’ market, Clara buys pounds of peaches and pounds of apples. Peaches cost $4 per pound and apples cost $3 per pound. The equation above represents the total cost, in dollars, of Clara’s purchase.
If Clara buys exactly 2 pounds of apples, how many pounds of peaches does she buy?
For SAT word problems that already give you an equation, first match each variable to what it represents in the story. Then plug in any values the problem gives (like a fixed number of pounds or a fixed price) for the appropriate variable to reduce the equation to one variable. Solve that simple linear equation carefully—do the arithmetic step by step—and finally check your answer by substituting it back into the original equation to ensure it makes the total come out correctly.
Hints
Identify the role of x and y
Look back at the problem statement: which variable represents pounds of peaches, and which represents pounds of apples?
Use the information about apples
The problem tells you Clara buys exactly 2 pounds of apples. Which variable should you replace with 2 in the equation ?
Solve the resulting equation
After substituting for , you will have an equation with only . First combine like terms, then isolate using inverse operations: subtract, then divide.
Desmos Guide
Use Desmos to compute x directly
In Desmos, type the expression (26 - 3*2)/4 and look at the numeric output. That output is the number of pounds of peaches Clara buys when she purchases 2 pounds of apples.
Step-by-step Explanation
Understand what the variables mean
From the context:
- = number of pounds of peaches
- = number of pounds of apples
The equation comes from:
- Peaches cost $4 per pound, so their cost is .
- Apples cost $3 per pound, so their cost is .
- The total cost is $26, so .
Substitute the given information
We are told Clara buys exactly 2 pounds of apples, so .
Substitute into the equation:
Now simplify the left side.
Simplify and isolate x
First, multiply :
Now solve this equation step by step:
- Subtract 6 from both sides:
- Divide both sides by 4:
This fraction simplifies to a whole number.
Find x and match the answer choice
Simplify :
So Clara buys 5 pounds of peaches. Among the choices given, this corresponds to C) 5.