SAT Math Practice Question with Detailed Solution

A food truck sells hamburgers for $8 each and hot dogs for $5 each. On Saturday, the truck sold a total of 95 items and made $640. How many hamburgers did the truck sell?

  1. 40
  2. 46
  3. 49
  4. 55

Step-by-Step SAT Math Solution

This free SAT practice question tests your ability to solve a system of linear equations, which is a common concept on the digital SAT math section. Let's break down the solution systematically:

Setting Up the System of Linear Equations

  1. First, let's define our variables:
    • Let x = number of hamburgers sold
    • Let y = number of hot dogs sold
  2. From the first condition, we know the total number of items sold:
    • x + y = 95 .... (Equation 1)
  3. From the second condition, we can find the total revenue:
    • Each hamburger costs $8, so revenue from sale of x hamburgers = 8x
    • Each hot dog costs $5, so revenue from sale of y hot dogs = 5y
    • Total revenue = $640
    • Therefore: 8x + 5y = 640 ... (Equation 2)

Solving the System with Elimination Method

This system can be solved efficiently using the elimination method, a key technique for SAT math problems:

  1. Multiply Equation 1 by 5:
    • 5(x + y = 95)
    • 5x + 5y = 475 ... (Equation 3)
  2. Subtract Equation 3 from Equation 2:
    • (8x + 5y = 640) - (5x + 5y = 475)
    • 3x = 165
  3. Solve for x:
    • x = 165 ÷ 3 = 55
  4. We can verify our answer by finding y:
    • From Equation 1: y = 95 - x = 95 - 55 = 40
    • Check: 8(55) + 5(40) = 440 + 200 = 640 ✓

Therefore, the food truck sold 55 hamburgers on Saturday.

The answer is D) 55.

How Important are These Questions on the SAT?

Systems of linear equations are a fundamental concept tested frequently on the SAT math section. These free SAT practice questions help you prepare for the new digital SAT format. When studying for the SAT, practicing these types of problems will strengthen your algebra skills and improve your problem-solving strategies.

This particular SAT practice problem also incorporates real-world applications of math, which is another common theme in SAT questions. Being able to translate word problems into mathematical equations is a crucial skill for SAT success.

For more free SAT practice questions and comprehensive SAT prep resources, continue exploring our SAT Question Bank and SAT study help blog.

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