Nine wonderful students decided to buy their math teacher an expensive present, each contributing the same amount of money. Four other students found out about the plan and joined in, agreeing to pay their share of the present's cost. This resulted in a saving of $33.32 for each of the original 9 students. The cost of the gift, in dollars, was?
cost of gift ---- x
cost for each of the nine originals = x/9
cost per student with 13 paying = x/13
x/9 - x/13 = 33.32/9
times 117
13x - 9x = 3898.44
4x = 3898.44
x = 974.61
check:
original share = 974.61/9 = 108.29
new share = 974.61/13 = 74.97
saving per share = 33.32 , as required
Well, it seems like these students are really good at math but not so great at buying presents. They managed to save $33.32 each, huh? Maybe they should have considered buying their teacher a calculator instead. Anyways, let's solve this math mystery.
We have a total of 9 + 4 = 13 students contributing money for the gift. Let's call the cost of the gift "x" dollars.
Since each of the original 9 students saved $33.32, we can write an equation:
9 * (x - 33.32) = 13x
Now, let me do some calculations. Bippity boppity boo, Fingers crossed, here's the answer for you!
9x - 299.88 = 13x
-4x = 299.88
x = -74.97
Oh no, it seems like the cost of the gift is -74.97 dollars! I knew they should have bought a calculator instead. It seems the numbers have gone a little wonky here. So, my friend, it seems there may be a mistake in the problem or some funny elephant math going on. That's all I can clown around with for now!
Let's first find the total number of students who decided to buy the gift. Initially, there were 9 students, and then an additional 4 students joined, resulting in a total of 9 + 4 = 13 students.
Next, let's assume that each student initially contributed x dollars toward the cost of the gift.
Since each of the original 9 students saved $33.32, the total savings by the 9 students would be 9 * $33.32 = $299.88.
The total cost of the gift would be the sum of the savings and the amount contributed by the additional 4 students, which is $299.88 + 4x.
Since each student initially contributed the same amount of money, the remaining 4 students would also contribute x dollars each. Therefore, the total amount contributed by the additional 4 students would be 4x.
Setting up an equation, we have:
$299.88 + 4x = 13x
Simplifying the equation, we have:
$299.88 = 9x
Dividing both sides by 9, we find:
x = $33.32
Therefore, each student initially contributed $33.32.
The cost of the gift would be the total savings by the original 9 students plus the contribution from the additional 4 students, which is $299.88 + 4 * $33.32 = $434.48.
Thus, the cost of the gift was $434.48.
To solve this problem, we need to set up an equation based on the given information.
Let's say the cost of the gift is 'x' dollars.
The original 9 students contributed 'x' dollars each, so a total of 9x dollars was collected.
When the additional 4 students joined in, the total number of students became 9 + 4 = 13. So, the 13 students contributed their share, which was (9x + 4x) = 13x dollars.
Given that the total savings for each of the original 9 students was $33.32, we can set up the equation as follows:
13x - 9x = 33.32
Combining like terms, we get:
4x = 33.32
Now, we can solve for 'x' by dividing both sides of the equation by 4:
x = 33.32 / 4
x ≈ 8.33
Therefore, the cost of the gift was approximately $8.33.