SOLUTION: 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= tru

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.
.
RELATED QUESTIONS
Erasers cost $6 per carton and pencils cost $7 per carton. If an order comes in for a... (answered by unlockmath)

Please help me solve this problem: Pencils cost $6 per carton and erasers cost $3 per... (answered by Tatiana_Stebko)

Using a manufacturer's coupon, Lucy bought 2 cartons of orange juice and received a third (answered by rfer)

A multinational company placed orders for printing papers and writing pads. In the first... (answered by CubeyThePenguin)

Chemical Products makes two insect repellents, Regular and Super. The chemical used for... (answered by josmiceli)

the total cost of n cartons of milk is $3.60. Each carton cost... (answered by harpazo)

A carton contains k boxes of paper cups and each box contains 100 paper cups. If the... (answered by jim_thompson5910)

lisa and berverly had just $5 to spend for an after school snack. they could have bought... (answered by stanbon)

Grace and hannah had just $5 to spend for an after-school snack. They could have 2... (answered by TimothyLamb)