A packet of chocolates contains pieces of milk, dark and orange chocolates. 25% of the chocolates are dark chocolates. The ratio of the number of dark chocolates to the number of milk chocolates is 5:7. There are 78 pieces of dark and orange chocolates. What is the total number of pieces of chocolates in the packet?

(1) 104

(2) 120

(3) 130

(4) 195

derpmcfearson Jul 1, 2024

#1**+1 **

We can first note somethings really important to solve this problem.

We can find the percentage of milk chocolates there is from the ratio. We have

\(25\% \cdot 7/5 = 5\% \cdot 7 = 35\%\)

Thus, 35% of the box is milk chocolate. Finally we know the amount of orange chocoaltes there are. We have

\(100\% - 25\% - 35\% = 40\%\)

Thus, 40% of the box is orange chocolates. Now, we can use the third condiditon stated in the problem.

Since dark and orange chocolates formed 78 pieces, let's find the percentage it is in total. We add the two up and we get

\(35\% + 45\% = 75\%\)

Thus, 75% of the box is equal to 78 pieces. We can now right the equation

\(3/4x = 78\) where x is the total amount of pieces. Thus, we have

\(x = 78 * 4/3\\ x = 26*4\\ x = 104\)

Thus our answer is 104 chocolates.

So choice 1 is our answer .

Thanks! :)

NotThatSmart Jul 1, 2024

#1**+1 **

Best Answer

We can first note somethings really important to solve this problem.

We can find the percentage of milk chocolates there is from the ratio. We have

\(25\% \cdot 7/5 = 5\% \cdot 7 = 35\%\)

Thus, 35% of the box is milk chocolate. Finally we know the amount of orange chocoaltes there are. We have

\(100\% - 25\% - 35\% = 40\%\)

Thus, 40% of the box is orange chocolates. Now, we can use the third condiditon stated in the problem.

Since dark and orange chocolates formed 78 pieces, let's find the percentage it is in total. We add the two up and we get

\(35\% + 45\% = 75\%\)

Thus, 75% of the box is equal to 78 pieces. We can now right the equation

\(3/4x = 78\) where x is the total amount of pieces. Thus, we have

\(x = 78 * 4/3\\ x = 26*4\\ x = 104\)

Thus our answer is 104 chocolates.

So choice 1 is our answer .

Thanks! :)

NotThatSmart Jul 1, 2024

#3**+1 **

Thanks, CPHill.

I just realized you could have just done \(100-25 = 75\%\) to find the total amount of orange and dark.

Then, we multiply the reciprocal of that by \(78\)

It gets the same answer of \(104\) since it's essentially the same steps. We still have

\(x = 78 * 4/3\\ x = 26*4\\ x = 104\)

It does save a few steps and is more efficient, but hey, same answer...

Thanks! :)

NotThatSmart
Jul 1, 2024