Please help! I'm in 6th grade. In this word problem, we're supposed to use a variable, and I'm completely lost 😣

Question

Caroline baked 3 dozen oatmeal raisin cookies for the bake sale at school. This is one fourth the number of cookies she baked in all. How many dozens of cookies did she bake in all?

Answer 1

Lucy,

youre lost; I’ll guide you back.

 

First, look at the problem and see if there are quantities that they talk about but you don’t know the number yet.

 

”cookies baked for a sale” is a quantity, but you know many there are: 36.

 

”cookies she baked in all” is a quantity but you DON’T know it. So this is an “unknown”, and we write an Abbreviation for it, and we call the abbreviation a “variable”. 

 

So, we say 

“Let x be the number of cookies baked in all”

That doesn’t solve the problem, but it makes it lots easier and quicker to talk about it.

 

So Let s try translating the words.

 

”Caroline baked 3 dozen oatmeal Raisin cookies...this is one fourth of the cookies she baked in all”

 

Those last few words are familiar, we’ve named that ”x”.

 

so let’s rewrite that sentence.

 

”Caroline baked 3 dozen oatmeal Raisin cookies...this is one fourth of x”

 

(I guess she made more cookies than just oatmeal raisin.)

 

Lets Translate a bit more: “one fourth” is also known as “1/4”

so the end of the sentence is now “...this is 1/4 x”

 

we can translate “is“ to “=“, and 3 dozen” to ”36”, and the rest of the words don’t matter

 

36 = 1/4 x

 

Here is an equation with the variable “x”, that means “number of cookies baked in all”.

 

Heres an approach to solving this equation. That means, here’s a way to find out the value of x, “the number of cookies baked in all”

 

I don’t know how far into algebra you have gone in sixth grade , so I’ll avoid Relying on your algebra knowledge. Instead, on a piece of paper draw a horizontal line roughly the length of your thumb. at the right end of the line, write ”36” under the end. 

 

You know that 36 is 1/4 of x, so make that line longer by drawing three more lines the same size. This is a number line, with a mark at 36, and it is 1/4 of the whole line. How would you find out how long the whole line is?

You would probably multiply 36 by 4. (You’d be right, go ahead and do it).

 

So, you’ve identified an “unknown”, you’ve abbreviated it with a “variable”, you’ve translate the words into an equation, and solved the equation for the number of cookies baked in all.

 

When you use algebra, you can solve more complicated equations more easily than by making number lines, but this is a start.

I hope this helps.

Answer 2

c represents the number of cookies she baked

36 (that's three dozen) is 1/4 of c

36 = (1/4)c

 

Can you solve for c and answer?