Resources

Resources

GCF and LCM: word problems

An astronomer observes the velocity of a galaxy at a distance of

100

\mathrm{Mpc}

) to calculate its distance two billion years from now using two different models. In the first model, the distance from the galaxy to Earth increases by

9 \mathrm{Mpc}

every billion years. In the second model, the distance from the galaxy to Earth increases by

10

percent every billion years. Two billion years from now, how much further would the galaxy be in the second model compared to the first model in megaparsecs?

In basketball, the number of points you score is given by

3 x+2 y+1 z

x

is threepointers,

y

is two-pointers, and

z

is free throws (one-pointers). What is the total number of points scored by a player who makes

3

5

two-pointers, and

6

Freddie's goal is to walk at least

25

kilometers a week. If he has already walked

13

6

kilometers this week, what is the minimum distance, in kilometers, he still needs to walk this week to meet his goal?

The Silver Lake Reservoir in California is being drained to make way for an underwater pipeline. The reservoir holds

400

million gallons of water, and it is estimated that the drainage will take at least

25

days. If the water is drained at a constant rate, what is the maximum rate of drainage, in millions of gallons per day?

3 x+2 y \geq 24

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Erica's goal is to score at least

24

points in her next playground basketball game. The given inequality represents this goal, where

x

is the number of

3

-point field goals she scores and

y

is the number of

2

-point field goals she scores. If she scores

53

-point field goals, what is the minimum number of

2

-point field goals she must score to meet her scoring goal?

Mindy and Troy combined ate

9

pieces of wedding cake. Mindy ate

3

pieces of cake and Troy had

\frac{1}{4}

of the total cake. How many pieces of cake were there in all?

300

-acre farm produced

20

000

bushels of corn last year. What is the minimum rate of production, in bushels per acre, that is needed this year so the farm's two-year production total will be at least

49

100

bushels of corn?

Walter is trying to control his home energy costs. His bill consists of a monthly flat fee of

\$ 9

\$ 0.07

per kilowatt hour of electricity used. If Walter does not want his electric bill to exceed

\$ 65

per month, what is the maximum whole number of kilowatt hours he can use?

The great snipe can fly up to

4

000

\mathrm{mi}

) without stopping for food or water at a speed of

60

miles per hour (mph). What is the maximum number of days, to the nearest tenth, that the great snipe can fly without stopping?

In the years from

2010

2015

, the basketball player LeBron James played

17

860

minutes, more than any other player in the National Basketball Association. Kevin Durant is second, with

15

595

minutes played in those years. If Kevin Durant averaged

38

minutes per game, what is the least number of additional games he would have had to play to surpass LeBron James's record? The answer should be a whole number.

Michael is planning to join a local gym and is researching his options. His first option, Bodies In Motion, charges a one time enrollment fee of

\$ 60.00

, plus an additional monthly fee of

\$ 18.00

. His second option, Cardio World, does not have an enrollment fee, but charges

\$ 30.00

per month. In how many months will the total cost for a gym membership at both gyms be equal?

Kris is wrapping Christmas lights around the railing that runs around three sides of his square porch If one side of his porch is

12

feet long, and each strand of his Christmas lights will wrap around a

70

-inch length of the railing, what is the minimum number of strands Kris needs to completely wrap the porch railing?

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6

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7

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8

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9