Question

A team of astronauts is preparing a mission to the moon. The pull of gravity on the moon is different than on Earth. On the moon, things weigh 16 of what they weigh on Earth. For this mission, each astronaut will bring x pounds of food and y pounds of gear. Which inequality correctly compares the weight of the supplies on the moon to the weight of the supplies on Earth, given that aa represents the number of astronauts going on the mission?a. xya²>1/3xya²

b. xya<1/3xya
c. xa+ya>1/6xa+1/6ya
d. 2axy>2/3axy

Answer 1

`(C)`
`xa+ya>(1)/(6)xa+(1)/(6)ya`

Explanation:

For this mission, each astronaut will bring

• x pounds of food; and
• y pounds of gear.

Weight of Supplies of One Astronaut on the earth = (x+y) pounds

If the total number of astronauts going on the mission= a

• Total Weight on the earth of the supplies of all the Astronaut
  `=a (x+y) pounds`

On the moon, things weigh
`(1)/(6)` of what they weigh on Earth.

• Total Weight of the supplies of all the Astronaut on the moon
  `=(1)/(6)a (x+y) pounds`

Therefore,the inequality which correctly compares the weight of the supplies on the moon to the weight of the supplies on Earth is:

`a (x+y) pounds >(1)/(6)a (x+y) pounds\\xa+ya>(1)/(6)xa+(1)/(6)ya`