PSAT Math Grid-Ins Question 9: Answer and Explanation

Question: 9

Mathew and Moriah purchased a tandem bicycle for $540. If the amount Moriah paid was $30 less than twice the amount Mathew paid, how much, in dollars, did Moriah pay?

(Disregard the dollar sign when gridding in your answer.)

Correct Answer: 350

Explanation:

350

The question asks for how much Moriah paid. Translate English into math to find how much Moriah paid. Moriah, m₁, and Mathew, m₂, paid a total of $540. In equation form, m₁ + m₂ = 540. The amount Moriah paid was $30 less than twice the amount Mathew paid. In equation form, m₁ = 2m₂ - 30. Plug the second equation into the first to get 2m₂ - 30 + m₂ = 540. Combine like terms to get 3m₂ - 30 = 540. Add 30 to both sides to get 3m₂ = 570. Divide both sides by 3 to get m₂ = 190. $190 is the amount Mathew paid. Moriah paid $540 - $190 = $350. The correct answer is 350.