Spiders and ants

Pro Problems > Math > Algebra > Equations > Systems of Equations > Word Problems

Spiders and ants

In my house there are both ants and spiders. Together there are 240 legs. If there were half as many spiders, and twice as many ants, there would be 336 legs. How many ants do I have in my house?

Presentation mode

Problem by Mr. Twitchell

Solution

In order to make it feasible for teachers to use these problems in their classwork, no solutions are publicly visible, so students cannot simply look up the answers. If you would like to view the solutions to these problems, you must have a Virtual Classroom subscription.

Assign this problem

Click here to assign this problem to your students.

Similar Problems

Difference System

The difference between two numbers is twice the smaller number. The smaller number is 10 less than the larger number. Find the smaller number.

Bag of Candy

Three children share a box of candy between them. Linda gets three times as many peppermints as Shannon, who gets 5 more licorice sticks than Yvette. Yvette gets three times as many licorice sticks as Linda, and half as many peppermints as Linda and Shannon combined. If Shannon got two more licorice sticks than peppermints, and there are 98 candies in all, how many peppermints were there?

Humpty Dumpty

Humpty Dumpty sat on a wall,

Humpty Dumpty had a great fall;

All the king's horses and all the king's men

Couldn't put Humpty together again.

The reason the king's horses and the king's men couldn't put Humpty Dumpty back together again is that the king's horses were no help whatsoever. In fact, the king's horses (who are not very handy) accidentally break pieces instead of putting them together.

One king's man can put together two pieces every 5 seconds.

One king's horse can break a piece in two every 2 seconds.

There are twenty more men than horses.

If there had been six fewer men, and horses broke pieces at a rate of one every three seconds, they could have done the job.

If the number of men and the number of horses are both prime numbers, how many men and horses are there?

A Sum of Sums

If the sum of an integer and the next consecutive integer is added to the sum of another integer and its next consecutive odd integer, the result is 71.

If the smaller of the two numbers is subtracted from twice the larger, the result is 29. What are the two numbers?

Three Digits by Sums

I am a three digit number. The sum of my first two digits is 15, and the sum of my last two digits is 8. The sum of my first and last digits is 7. What number am I?

Difference and Sum

Two numbers add to twenty-seven more than the opposite of the smaller number. The numbers differ by three. What is the larger number?

Handshakes

Mr. T wants each of his math students to shake hands with each of his other math students exactly once. He also wants each of his math students to shake Mr. H's hand twice. Mr. T shakes Mr. H's hand once. If there were 78 handshakes in all, how many math students does Mr. T have?