Home / Digital SAT Math: Linear inequalities in one or two variables – Practice Questions

Digital SAT Math: Linear inequalities in one or two variables – Practice Questions

Digital SAT Math: Linear inequalities in one or two variables - Practice Questions - New Syllabus

DSAT MAth Practice questions – all topics

  • Algebra Weightage: 35%  Questions: 13-15
    • Linear equations in one variable
    • Linear equations in two variables
    • Linear functions
    • Systems of two linear equations in two variables
    • Linear inequalities in one or two variables

DSAT MAth and English  – full syllabus practice tests

Question Easy

On a car trip, Rhett and Jessica each drove for part of the trip, and the total distance they drove was under 220 miles. Rhett drove at an average speed of 35 miles per hour (mph), and Jessica drove at an average speed of 40 mph. Which of the following inequalities represents this situation, where \( r \) is the number of hours Rhett drove and \( j \) is the number of hours Jessica drove?

A. \( 35r + 40j > 220 \)

B. \( 35r + 40j < 220 \)

C. \( 40r + 35j > 220 \)

D. \( 40r + 35j < 220 \)

▶️ Answer/Explanation
Solution

Ans: B

Rhett’s distance: \( 35r \) (35 mph \(\times\) \( r \) hours).

Jessica’s distance: \( 40j \) (40 mph \(\times\) \( j \) hours).

Total distance under 220 miles: \( 35r + 40j < 220 \).

Choice A: Incorrect, uses \( > \) instead of \( < \).

Choice C: Incorrect, swaps speeds and uses \( > \).

Choice D: Incorrect, swaps speeds.

Question Easy

An elementary school teacher is ordering \( x \) workbooks and \( y \) sets of flash cards for a math class. The teacher must order at least 20 items, but the total cost of the order must not be over \($80\). If the workbooks cost \($3\) each and the flash cards cost \($4\) per set, which of the following systems of inequalities models this situation?

A. \( x + y \geq 20 \)
\( 3x + 4y \leq 80 \)

B. \( x + y \geq 20 \)
\( 3x + 4y \geq 80 \)

C. \( 3x + 4y \leq 80 \)
\( x + y \geq 20 \)

D. \( x + y \leq 20 \)
\( 3x + 4y \geq 80 \)

▶️ Answer/Explanation
Solution

Ans: A

Total items: \( x + y \geq 20 \) (at least 20 items).

Cost: \( 3x \) (workbooks at \($3\)) + \( 4y \) (flash cards at \($4\)) \(\leq 80\).

Thus: \( 3x + 4y \leq 80 \).

Choice B: Incorrect, uses \( \geq 80 \).

Choice C: Same as A, but order doesn’t affect correctness.

Choice D: Incorrect, uses \( \leq 20 \) and \( \geq 80 \).

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