Question 105594: Dolls cost $140 per carton and trucks cost $430 per carton. If an order comes in for a total of 100 cartons for $28,500, what was the number of cartons of dolls? (Hint, Let T= trucks)
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let D equal 1 carton of dolls and T equal 1 carton of trucks. The problem says that the
combined numbers of cartons is 100. Therefore, if we add D and T the total number of cartons
is 100. In equation form this is:
.
D + T = 100
.
Since the dolls cost $140 per carton, if we multiply the number of cartons of dolls by
$140, we have the total amount of money spent on dolls. Therefore, $140N is the amount
spent on dolls.
.
Similarly, trucks are $430 per carton. Therefore, the total amount spent on trucks is $430
times the number of cartons of trucks that were purchased.
.
When you add these two amounts together the total is $28,500. In equation form this is:
.
140D + 430T = 28,500
.
But from the very first equation we set up (D + T = 100) we can subtract T from both sides
to get D = 100 - T. This means that we can substitute 100 - T for D in the "money"
equation. When we make this substitution, the money equation becomes:
.
140*(100 - T) + 430T = 28500
.
Doing the multiplication on the left side results in:
.
14000 - 140T + 430T = 28500
.
If you combine the two terms containing T on the left side you get 430T - 140T = 290T. This
makes the equation become:
.
14000 + 290T = 28500
.
Then get rid of the 14000 on the left side by subtracting 14000 from both sides to reduce
the equation to:
.
290T = 14,500
.
Solve for T by dividing both sides by 290 and you have:
.
T = 14500/290 = 50
.
This says that there are 50 cartons of trucks. Since the total number of cartons is 100, that
means that there also must be 50 cartons of dolls.
.
Check using the money relationship. 50 cartons of dolls at $140 per carton multiplies
out to be $7000. And 50 cartons of trucks at $430 per carton multiplies out to be $21500. Adding
these two amounts results in $7000 + $21500 = $28500 and that total is what the problem
says it should be. Therefore, the answer of 50 cartons of dolls and 50 cartons of trucks
is correct. Hope this helps you to understand the problem and how to get the answer.
.
|
|
|
