+22 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
+1953 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%⋅7/5=5%⋅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∗4/3x=26∗4x=104
Thus our answer is 104 chocolates.
So choice 1 is our answer .
Thanks! :)
+1953 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%⋅7/5=5%⋅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∗4/3x=26∗4x=104
Thus our answer is 104 chocolates.
So choice 1 is our answer .
Thanks! :)
+1953 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∗4/3x=26∗4x=104
It does save a few steps and is more efficient, but hey, same answer...
Thanks! :)
