Question

At Megapolis Hospital one year, multiple-birth statistics were as follows: Sets of twins, triplets, and quadruplets accounted for $1000$ of the babies born. There were four times as many sets of triplets as sets of quadruplets, and there were three times as many sets of twins as sets of triplets. How many of these $1000$ babies were in sets of quadruplets?

$\ 25$

$\ 40$

$\ 64$

$\ 100$

$\ 160$

Answer: D

Concepts:system of equations

Difficulty rating: 1140

Solution:

Let $w,r,q$ be the numbers of sets of twins, triplets, and quadruplets. Then $2w+3r+4q=1000.$ The statement gives $r=4q$ and $w=3r=12q$ .

Substituting gives $2(12q)+3(4q)+4q$ $=40q=1000$ , so $q=25$ . The number of babies in sets of quadruplets is $4q=100$ .

Thus, the correct answer is D.

2016 AMC 10B Problem 13

Answer: D

Difficulty rating: 1140

Solution:

Problem 13 in Other Years