postillan4

2021-03-05

Carlos has at least as many action figures in his collection as Josh. Carlos has 5 complete sets plus 4 individual figures. Josh has 3 complete sets plus 14 individual figures. Which inequality represents how many action figures can be in a complete set?

Roosevelt Houghton

Let x be the number of action figures in a complete set.
Carlos has 5 complete sets so he has 5x action figures that are part of complete sets. He also has 4 individual action figures so the total number of action figures he has is 5x+4.
John has 3 complete sets so he has 3x action figures that are part of complete sets. He also has 14 individual figures so the total number of action figures he has is 3x+14.
If Carlos has at least as many action figures as Josh, then the total number of action figures that Carlos has must be greater than or equal to the total number of action figures that John has. Therefore, $5x+4\ge 3x+14$. Solving this inequality for x gives:
$5x+4\ge 3x+14$
$2x+4\ge 14$
$2x\ge 10$
$x\ge 5$
Subtract 3x on both sides. Subtract 4 on both sides. Divide both sides by 2.
The inequality that represents how many action figures can be in a complete set is then $x\ge 5x\ge 5.$

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