document.write( "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) \n" ); document.write( "
Algebra.Com's Answer #76854 by bucky(2189)![]() ![]() ![]() 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 \n" ); document.write( "combined numbers of cartons is 100. Therefore, if we add D and T the total number of cartons \n" ); document.write( "is 100. In equation form this is: \n" ); document.write( ". \n" ); document.write( "D + T = 100 \n" ); document.write( ". \n" ); document.write( "Since the dolls cost $140 per carton, if we multiply the number of cartons of dolls by \n" ); document.write( "$140, we have the total amount of money spent on dolls. Therefore, $140N is the amount \n" ); document.write( "spent on dolls. \n" ); document.write( ". \n" ); document.write( "Similarly, trucks are $430 per carton. Therefore, the total amount spent on trucks is $430 \n" ); document.write( "times the number of cartons of trucks that were purchased. \n" ); document.write( ". \n" ); document.write( "When you add these two amounts together the total is $28,500. In equation form this is: \n" ); document.write( ". \n" ); document.write( "140D + 430T = 28,500 \n" ); document.write( ". \n" ); document.write( "But from the very first equation we set up (D + T = 100) we can subtract T from both sides \n" ); document.write( "to get D = 100 - T. This means that we can substitute 100 - T for D in the \"money\" \n" ); document.write( "equation. When we make this substitution, the money equation becomes: \n" ); document.write( ". \n" ); document.write( "140*(100 - T) + 430T = 28500 \n" ); document.write( ". \n" ); document.write( "Doing the multiplication on the left side results in: \n" ); document.write( ". \n" ); document.write( "14000 - 140T + 430T = 28500 \n" ); document.write( ". \n" ); document.write( "If you combine the two terms containing T on the left side you get 430T - 140T = 290T. This \n" ); document.write( "makes the equation become: \n" ); document.write( ". \n" ); document.write( "14000 + 290T = 28500 \n" ); document.write( ". \n" ); document.write( "Then get rid of the 14000 on the left side by subtracting 14000 from both sides to reduce \n" ); document.write( "the equation to: \n" ); document.write( ". \n" ); document.write( "290T = 14,500 \n" ); document.write( ". \n" ); document.write( "Solve for T by dividing both sides by 290 and you have: \n" ); document.write( ". \n" ); document.write( "T = 14500/290 = 50 \n" ); document.write( ". \n" ); document.write( "This says that there are 50 cartons of trucks. Since the total number of cartons is 100, that \n" ); document.write( "means that there also must be 50 cartons of dolls. \n" ); document.write( ". \n" ); document.write( "Check using the money relationship. 50 cartons of dolls at $140 per carton multiplies \n" ); document.write( "out to be $7000. And 50 cartons of trucks at $430 per carton multiplies out to be $21500. Adding \n" ); document.write( "these two amounts results in $7000 + $21500 = $28500 and that total is what the problem \n" ); document.write( "says it should be. Therefore, the answer of 50 cartons of dolls and 50 cartons of trucks \n" ); document.write( "is correct. Hope this helps you to understand the problem and how to get the answer. \n" ); document.write( ". \n" ); document.write( " |