Word Problems!

Do the following word problems.

Make sure you write down your answer first. Then click the picture to show the answer and an explanation of the steps to getting the answer.

1.

A group of 120 students went to an amusement park.

The two most famous rides at the park are the Upchuck Express and the Barf-o-Rama.

Two-fifths of the group waited in line for the Upchuck Express.

The rest of the group waited in line for the Barf-o-Rama.

A single ride on the Upchuck Express lasts for 10 minutes and can take 8 kids at a time.

A single ride on the Barf-o-Rama lasts 8 minutes and can take 12 kids at a time.

Which group will finish their ride first?

Answer: the Barf-o-Rama group.

Find 2/5 of 120 students. One way to do this is find 1/5 of 120, and then double your answer. To find 1/5 of 120, simply divide 120 ÷ 5 = 24. So 2/5 of 120 = 48 students chose the Upchuck Express.

To find how many chose the Barf-o-Rama, simply subtract 120 - 48 = 72.

Next, we figure out how long the 48 students took to go through the Upchuck Express. We know it can take 8 kids at a time. So we divide 48 ÷ 8 = 6 trips. Each trip takes 10 minutes. So we multiply 6 x 10 = 60 minutes for all 48 students to finish the Upchuck Express ride.

Then we do the same for the Barf-o-Rama. 72 ÷ 12 = 6 trips. 6 x 8 = 48 minutes total for the Barf-o-Rama. That's less than the 60 minutes for the other ride.

2.

It is 7 miles from DJ's home to the Veggie Drink Shack.

On the way there, he can only cycle at a speed of 14 miles per hour.

On the way back, though, he can cycle at a speed of 21 miles per hour, since he will have drunk a Green Energy Smash drink.

He leaves his house at 6pm.

How long can DJ hang out at the Veggie Drink Shack if he wants to be home by 8pm?

Answer: One hour and ten minutes (or 70 minutes)

First, we need to figure out how long DJ will spend cycling. On the way, he's going at 14 miles per hour, but he only needs to cover 7 miles. That's half of 14, so it will take him a half-hour, 30 minutes.

On the way back, he'll be going at 21 miles per hour, but only needs to cover 7 miles. That's one-third of 21, so it will only take him one-third of an hour, or 20 minutes (20 is one-third of 60). So the total time spent cycling is 30 + 20 minutes, or 50 minutes total.

So now we need to figure out how long he can stay at the Veggie Drink Shack. He leaves at 6pm and wants to be back at 8pm, which is 2 hours (or 120 minutes) for the whole trip. If we subtract his travel time (50 minutes) from this 2 hours (120 minutes), we are left with 120 - 50 = 70 minutes, or one hour and ten minutes he can spend hanging out at the Veggie Drink Shack.

3.

Mr. Capra is throwing a goat-themed party for 60 of his closest friends and relatives.

He is saving up to buy his own flock of goats, so he doesn't want to buy any more food than he has to.

He is limiting each person to 2 goatburgers, 2 goat cheese lumps, and 1 individual-sized carton of goat milk.

Goatburgers come in packs of 8, goat cheese lumps in packs of 10, and goat milk cartons in packs of 12.

How many packages of each should Mr. Capra buy?

Answer: 15 packages of goatburgers; 12 packages of goat cheese lumps; 5 packages of goat milk cartons.

First, we need to figure out how much of each item he needs. There are 60 people; each gets 2 goatburgers. That's 60 x 2 = 120 goatburgers. Same for goat cheese lumps; he'll need 120 goat cheese lumps. And each person gets 1 carton of goat milk; that's 60 cartons of goat milk.

Next, we divide each total by the number of that item included in a package. So we divide 120 ÷ 8 = 15 packages of goatburgers. 120 ÷ 10 = 12 packages of goat cheese lumps. And 60 ÷ 12 = 5 packages of goat milk cartons.

4.

Peter can't decide...banjo music or yellow-bellied sapsuckers?

He is comparing the Twangers banjo club with the Sapsuckers bird-watching club.

The Twangers has a sign-up cost of $160 and monthly fees of $39.

The Sapsuckers has a sign-up cost of $250 and monthly fees of $32.

Which club offers the best value for a single year of membership?

How much would Peter save by going with this club?

Answer: the Twangers club. Peter would save $6.

We need to figure out how much each club would cost for a whole year. The Twangers has a monthly fee of $39. You'll pay that 12 times in a year. So we multiply: 12 x 39 = $468. Additionally, for the Twangers you pay the sign-up fee of $160. So we add that: 468 + 160 = $628 for the total cost for the Twangers club.

We'll do the same with the Sapsuckers. We take the monthly fee and multiply: $32 x 12 = $384 in monthly fees for the year. Then we add the sign-up fee: 384 + 250 = $634 for the total cost for the Sapsuckers club.

So we see that the Twangers banjo club is the better value. We subtract: 634 - 628 = $6 difference between the two.

NOTE: yellow-bellied sapsuckers are real.

5.

A previously unknown tribe has been contacted in the jungles of Brazil. They have an unusual measuring system.

In their system, 2 waknaks are as long as 5 bliplips.

10 bliplips are as long as 28 umpas.

How many umpas are as long as 3 waknaks?

Answer: 21 umpas are as long as 3 waknaks.

To start, let's look at the second statement: 10 bliplips = 28 umpas. We could rewrite that as 5 bliplips = 14 umpas, just by dividing each side by 2.

Do you see why that's useful? Look at the first statement. We see that 5 bliplips = 2 waknaks. Since 5 bliplips also = 14 umpas, then we can say that 2 waknaks = 14 umpas.

That means that 1 waknak = 7 umpas. The question is, how many umpas are in 3 waknaks? We would multiply 3 x 7 = 21. So 21 umpas are as long as 3 waknaks.