MathDB

4

Part of 2017 AMC 10

Problems(2)

Mia's Toys

Source: Problem #4 2017 AMC 10A

2/8/2017
Mia is “helping” her mom pick up 3030 toys that are strewn on the floor. Mia’s mom manages to put 33 toys into the toy box every 3030 seconds, but each time immediately after those 3030 seconds have elapsed, Mia takes 22 toys out of the box. How much time, in minutes, will it take Mia and her mom to put all 3030 toys into the box for the first time?
<spanclass=′latex−bold′>(A)</span> 13.5<spanclass=′latex−bold′>(B)</span> 14<spanclass=′latex−bold′>(C)</span> 14.5<spanclass=′latex−bold′>(D)</span> 15<spanclass=′latex−bold′>(E)</span> 15.5<span class='latex-bold'>(A)</span>\ 13.5\qquad<span class='latex-bold'>(B)</span>\ 14\qquad<span class='latex-bold'>(C)</span>\ 14.5\qquad<span class='latex-bold'>(D)</span>\ 15\qquad<span class='latex-bold'>(E)</span>\ 15.5
AMCAMC 10AMC 10 A2017 AMC 10Arate problemsrates
Fractions

Source: 2017 AMC 10B #4, AMC 12B #3

2/16/2017
Suppose that xx and yy are nonzero real numbers such that 3x+yx−3y=−2.\frac{3x+y}{x-3y}= -2. What is the value of x+3y3x−y?\frac{x+3y}{3x-y}?
<spanclass=′latex−bold′>(A)</span>−3<spanclass=′latex−bold′>(B)</span>−1<spanclass=′latex−bold′>(C)</span>1<spanclass=′latex−bold′>(D)</span>2<spanclass=′latex−bold′>(E)</span>3<span class='latex-bold'>(A) </span> {-3} \qquad <span class='latex-bold'>(B) </span> {-1} \qquad <span class='latex-bold'>(C) </span> 1 \qquad <span class='latex-bold'>(D) </span>2 \qquad <span class='latex-bold'>(E) </span> 3
AMC 10 BAMC 12 B2017 AMC 10B2017 AMC 12BAMCalgebra