Question

Dear Mitch,

You're probably getting sick of them, but in my class we've been having a good time working out those balance scale problems. Do you think you could post a couple more before you stop them?

Thank you,

Rickey Johnson

Answer

Dear Rickey,

I'm not sick of them at all!

(For lots of reasons, they are one of the most enjoyable types of problems for me to come up with, but of course we try to spread things around to hit as many different areas as possible.)

For the balance scale problems, one doesn't need much (or any) formal training in algebra or any other kind of math to come up with a solution, but CLEARLY the tougher ones are easier to do if a person does have some experience. First, though, as you will see when you scroll down, we are posting two more!

(But first, here's a couple of the more traditional style multiple choice questions to give students practice with the type they are going to have to be able to do on standardized tests!)

Then, after reading these two, please do not forget to continue scrolling down and down and down and down... for those balance questions. Have fun!

1.

A certain Valentine's Day cookie comes in 2 colors, pink and purple.

They come in shrink-wrapped packages in this ratio: 3 pink to every 4 purple.

Mrs. H.B. Huffingmeyer-Fitzwhalen is having a big Valentine's Day party for her daughter, Fluffy, and she does not want to be caught short, so she loads up her cart as high as she can in the store with only these popular cookies.

** QUESTION**:

How many cookies altogether can Mrs. H.B. Huffingmeyer-Fitzwhalen have in her cart when she finally finishes at the checkout line?

A) 80

B) 81

C) 82

D) 83

E) 84

2.

At a Valentine's Day Party, 2/3 of the guests ate only pink cookies, 1/4 of the guests ate only red cookies, and no guest ate both red cookies and pink cookies.

__QUESTION__:

If there were 5 other guests at the party who ate no cookies, then how many guests were at the party?

A) 25

B) 30

C) 45

D) 50

E) 60

Now, as youwill see, one of these (the first one) has a ** Valentine's Day** theme.

The second one, which is just beneath it as continue scrolling downward, has a ** Presidents' Day** theme.

Hope they are as fun for you and your classmates as the previous ones!

And while you are working on them, the most important thing is to have a pleasant holiday season!

HERE THEY ARE:

__ VALENTINE'S DAY BALANCE CHALLENGE__:

A series of weighings is shown here. The items on the scales are pink hearts, red hearts, and purple hearts. Each color represents a different kind of candy, so hearts of each color weigh the same amount as other hearts of the same color, but weigh a different amount from the hearts of any other color!

The first two scales (scale A and scale B) are balanced and complete. But the third scale (scale C) is not.

** QUESTION**: Based on what you see below, how many PINK hearts would you need to place on the right-hand side of scale C in order to form a balance with the 6 PURPLE hearts and the 2 RED hearts on the left-hand side of that scale?

__ PRESIDENTS' DAY BALANCE CHALLENGE__:

A series of weighings is shown here. The items on the scales are paperweights designed to celebrate Presidents' Day. There are three kinds of paperweights: "United States flags", "Liberty Bells", and small replicas of George Washington's head.

The first two scales (scale A and scale B) are balanced and complete. But the third scale (scale C) is not.

**: Based on what you see below, how many George Washington paperweights would you need to place on the right-hand side of scale C in order to form a balance with the 3 "liberty bells" and the 1 "flag" on the left-hand side of that scale?**

__QUESTION__