Question

The friends are making cookies for the bake sale. They baked 3/5 of their cookies on Monday. They baked 2 dozen on Tuesday. If they still have 1/3 of their cookies left to bake, how many cookies are they planning to bake in all? (PLEASE SHOW STEPS!)

Answer 1

Let's define our variables first
M = Monday
T = Tuesday
W = Wednesday (or the day when they make the remainder of their cookies)

The problem tells us:
M = 3/5 (M + T + W)
T = 24
W = 1/3 (M + T + W)

Let's simplify M and W by using (M + T + W):
5/3 M = (M + T + W)
3 W = (M + T + W)
5/3 M = 3 W
5/9 M = W

Let's plug W back into our initial equations:
M = 3/5(M + 24 + 5/9M)
M = (3/5)M + (72/3) + (1/3)M
(15/15)M = (9/15)M + (72/3) + (5/15)M
(15/15)M = (14/15)M + (72/3)
1/15M = 72/3
M = 216

Plugging in all the numbers:
W = 5/9(216)
W = 120
T = 24
M = 216

Total cookies = 360

Answer 2

These girls really need to get their cookie situation organized!

Alright, so... first let's get this problem into a simpler form.

They made 3/5 of the total, then 2 dozen which = 24 and they still have to make 1/3 more.

So to make 3/5 and 1/3 more compatible, find the LCM of the Denominator. This = 15. 5*3=15 so take 3 (from 3/5) and multiply by 3, which is 9.

This turns 3/5 to 9/15

Then do the same to the other fraction. The Denominator (3) x 5 = 15, so take the Numerator (1)x5= 5.

This turns 1/3 to 5/15

Now that this is a little more clear, let's look at the problem with our equal and substituted values.

They made 9/15 of the total, then 2 dozen which = 24 and they still have to make 5/15 more.

So from this, we can see that after they made 24 (2 Dozen) that they need 5/15 more. 15/15 would mean they're done, so that minus 5/15 = 10/15.

The difference from 9/15 & 10/15 is 1/15. This is how much was added when they made 24 more. So now we know that 1/15=24.

With this information, we can finally solve the problem.

They plan to bake 15/15 of the cookies. This is just a term that is equal to 1 whole. The "whole" is the whole amount of cookies being baked. Since 1/15=24, we can figure out 15/15 by taking 15x24.

15 x 24 = 360. So they made 360 cookies. Sounds delicious.

I hope this helped! And hopefully these imaginary friends sell all 360 cookies!