MathDB

7

Part of 2019 AMC 10

Problems(2)

Slopes and Shoelace

Source: 2019 AMC 10A #7 / AMC 12A #5

2/8/2019
Two lines with slopes 12\dfrac{1}{2} and 22 intersect at (2,2)(2,2). What is the area of the triangle enclosed by these two lines and the line x+y=10?x+y=10 ?
<spanclass=′latex−bold′>(A)</span>4<spanclass=′latex−bold′>(B)</span>42<spanclass=′latex−bold′>(C)</span>6<spanclass=′latex−bold′>(D)</span>8<spanclass=′latex−bold′>(E)</span>62<span class='latex-bold'>(A) </span> 4 \qquad<span class='latex-bold'>(B) </span> 4\sqrt{2} \qquad<span class='latex-bold'>(C) </span> 6 \qquad<span class='latex-bold'>(D) </span> 8 \qquad<span class='latex-bold'>(E) </span> 6\sqrt{2}
AMC
Casper the Candy-Loving Ghost

Source: 2019 AMC 10B #7/12B #5

2/14/2019
Each piece of candy in a store costs a whole number of cents. Casper has exactly enough money to buy either 12 pieces of red candy, 14 pieces of green candy, 15 pieces of blue candy, or nn pieces of purple candy. A piece of purple candy costs 20 cents. What is the smallest possible value of nn?
<spanclass=′latex−bold′>(A)</span>18<spanclass=′latex−bold′>(B)</span>21<spanclass=′latex−bold′>(C)</span>24<spanclass=′latex−bold′>(D)</span>25<spanclass=′latex−bold′>(E)</span>28<span class='latex-bold'>(A) </span> 18 \qquad <span class='latex-bold'>(B) </span> 21 \qquad <span class='latex-bold'>(C) </span> 24\qquad <span class='latex-bold'>(D) </span> 25 \qquad <span class='latex-bold'>(E) </span> 28