supremecheetah

Problem: Carlos baked a dozen cupcakes for the village fete. Half the cakes had pink icing and half had blue icing. Two of the cakes with blue icing and 3 cakes that had pink icing had a cherry on top. The rest of the pink cakes and 1 of the blue cakes had chocolate sprinkles on. The cakes without cherries on top were in white cases and the rest were in green cases. How many cakes were in white cases?

Given:

12 cupcakes

1/2 pink and 1/2 blue so 6 pink cupcakes and 6 blue cupcakes

2 cakes blue icing

3 cakes pink icing and cherry

x pink cake(s) and 1 blue cake had chocolate sprinkles

Cakes w/ cherry white cases and cakes without cherry green cases

Solution: This is a problem where many unnecessary information is given, so we need to only use the information we need to solve this problem. To find how many cakes were in white cases, let us find how many cakes were in green cases. 5 cakes were in green cases because the problem stated, "two of the cakes with blue icing and 3 cakes that had pink icing had a cherry on top." So the number of cakes in white cases is 12 - 5 = 7 cupcakes.

Me neither. Do you know why it isn't 17/7?

I can only help with the systems of equations part. I'm not sure after that.

Please don't be rude @guest with the "your mom" joke.

@SportzGuy2310 I agree with your answer! This is how I did it:

Let candy bar = c and bubble gum = b.

Now let's set up the equation: c+b = 1.50

And we are also given: c = 1+b

Now let's plug in c=1+b into c+b = 1.50

We get: 1+b+b = 1.50 ⟹ 2b+1 = 1.50 ⟹ 2b = 0.50 ⟹ b = 0.25

Therefore, the cost of a bubble gum is $0.25.

Which inequalities??

A+n=7B

A-n=3B

2A=10B

Try to see if you can find the answer from there? If not, I will give you the solution. (I still think 17/7 is the correct answer though.)

Agreed! I was going to post one but yours is already detailed!

1. 6-8-10 is a pythagreon triple so the area would be (6*8)/2 = 48/2 = 24. But if you don't know that 6-8-10 is 3-4-5 multiplied by 2, you can use the pythagreon theorem to find the third side: sqrt(6^2 + 8^2) = sqrt(36+64) = sqrt(100) = 10 and find the area the same way from that.

2. The triangle sum theorem states the three angles in a triangle sum to 180 degrees. Since we know two angles, the third one must be: 135+30+x=180 ⟹ 165+x=180 ⟹ x = 180-165 ⟹ x = 15. Therefore angle BAC = 15 degrees.

I got 1920 @SportzGuy2310 when I expanded it using the binomial theorem.

Assume:

the # of yellow marbles is x

the # of green marbles is 2x

the # of blue marbles is 3x

the # of white marbles is 4x

x+2x+3x+4x=180

10x = 180 

x = 18

the # of blue marbles = 3x = 3(18) = 54 marbles

And your solution is incorrect, the correct answer is 940. You would have to use multiplicative inverses in your solution.

What is CRT + MMI?

Good job!