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Test
Math
Domain
Algebra
Skill
Linear inequalities in one or two variables
Difficulty
Easy
ID: 2c121b25
Modded SAT Question Bank by Abdullah Mallik

Valentina bought two containers of beads. In the first container 30% of the beads are red, and in the second container 70% of the beads are red. Together, the containers have at least 400 red beads. Which inequality shows this relationship, where x is the total number of beads in the first container and y is the total number of beads in the second container?

  1. 0 point 3 x, plus, 0 point 7 y, is greater than or equal to, 400
  2. 0 point 7 x, plus, 0 point 3 y, is less than or equal to, 400
  3. the fraction x over 3, end fraction, plus, the fraction y over 7, end fraction, is less than or equal to, 400
  4. 30 x, plus, 70 y, is greater than or equal to, 400
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Correct Answer: A
Rationale

Choice A is correct. It is given that x is the total number of beads in the first container and that 30% of those beads are red; therefore, the expression 0.3x represents the number of red beads in the first container. It is given that y is the total number of beads in the second container and that 70% of those beads are red; therefore, the expression 0.7y represents the number of red beads in the second container. It is also given that, together, the containers have at least 400 red beads, so the inequality that shows this relationship is 0.3x + 0.7y ≥ 400.

Choice B is incorrect because it represents the containers having a total of at most, rather than at least, 400 red beads. Choice C is incorrect and may be the result of misunderstanding how to represent a percentage of beads in each container. Also, the inequality shows the containers having a combined total of at most, rather than at least, 400 red beads. Choice D is incorrect because the percentages were not converted to decimals.

Question Difficulty: Easy
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