if gina made a total of $125 and only sold 17 items, how many cookies did gina sell?

Question

gina sold cookies and cakes. cookies sold for $7 each while the cakes sold for $10 each.

Answer 1

Hi Brianna C.,

Let me walk you through the general method for solving "word problems" like this one, then you can solve this or really any other word problem easily!

It helps to write down the information you are given, first of all -- that will focus you on what you know, and point up, perhaps, what you don't yet know. Also, it will prevent you from hasty misreadings of the problem (and believe me, even old scientists occasionally misread problems!).

So in this case, you might write down:

Total sale proceeds = $125

Each cookie sale = $7

Each cake sale = $10

Total number of items sold = 17

Now, look at what you are asked to find out: numbers of cookies and cakes sold, each.

At this point, you do what you always must do: assign a variable to one of the pieces of information you don't yet know, but want to know. Why do you do this? Because you can push a variable around in a mathematical way (using operations of arithmetic, equations, inequalities, etc.), which your brain doesn't allow you to do as a text idea (nobody's brain can, don't worry!).

Now, sometimes it matters just which piece of information you pick for this, and sometimes it doesn't, or sometimes it's just faster to get the results if you pick one vs. another. You will get a sense of this as you get more experience; but, at the very least, you can not go wrong by making a choice on this!

So, let's arbitrarily assign the number of cookies sold to the variable x . Note that this is not the multiplication sign; if you need to, underline it to distinguish it, as you work with it. Or, just use (), *, or • to show multiplication, instead of a "x".

Now, you can start to relate the information you already have, into a unified whole.

In this case, since the total number of items sold was 17, there must be (17-x) cakes sold. Right?

Next, what do you know? Total sales!, and that is made up of sales of cookies plus sales of cakes, right?

So write that as an equation: (drop the $ sign, all money will be figured as $ in the equation):

7*x + 10*(17-x) = 125

[That's because each item type sales revenue is the number of it sold, times the selling price/each.]

Now you ruthlessly practice your math skills: Do the multiplications, and regroupings, etc., to solve for x:

7x +170 - 10x = 125

-3x = -45

3x = 45

x = 15

Thus, 15 cookies were sold, and 2 cakes.

A few general notes to conclude: Sometimes you need to assign more than one variable in a problem. Whenever possible, only assign one; since the number of cakes and cookies are related to each other (adding to 17 items total), therefore you can get by here with only one. IF you assign 2 variables, you need 2 independent equations to solve (= to obtain a single unique answer for each variable). But you probably already know how to solve those pairs of equations (substitution, elimination of a variable, etc.).

-- Cheers, -- Mr. d.