document.write( "Question 417759: A manufacturer produces three types of radios: deluxe, standard and economy. Each radio uses three different types of transistors: P, Q and R. The deluxe radio uses 2 P's, 7 Q's and 1 R. The standard contains 2 P's, 3 Q's and 1 R, and the economy model requires 1 P, 2 Q's and 2 R's.\r
\n" ); document.write( "\n" ); document.write( "How many radios of each type can be constructed if the total number of transistors (P's, Q's and R's) available are 2200, 3400 and 1400 respectively and all transistors must be used?\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #292531 by ankor@dixie-net.com(22740)\"\" \"About 
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A manufacturer produces three types of radios: deluxe, standard and economy.
\n" ); document.write( " Each radio uses three different types of transistors: P, Q and R.
\n" ); document.write( " The deluxe radio uses 2 P's, 7 Q's and 1 R.
\n" ); document.write( "The standard contains 2 P's, 3 Q's and 1 R, and
\n" ); document.write( " the economy model requires 1 P, 2 Q's and 2 R's.\r
\n" ); document.write( "\n" ); document.write( "How many radios of each type can be constructed if the total number of transistors (P's, Q's and R's) available are 2200, 3400 and 1400 respectively and all transistors must be used?
\n" ); document.write( ":
\n" ); document.write( "Let d = no. of deluxe radios
\n" ); document.write( "Let s = no. of standard radios
\n" ); document.write( "let e = no. of cheap radios
\n" ); document.write( ":
\n" ); document.write( "Write a equation for each type of transistor
\n" ); document.write( "2d + 2s + 1e = 2200; the P trans
\n" ); document.write( "7d + 3s + 2e = 3400; the Q trans
\n" ); document.write( "1d + 1s + 2e = 1400; the R trans
\n" ); document.write( ":
\n" ); document.write( "multiply the 3rd equation by 2, subtract the 1st equation
\n" ); document.write( "2d + 2s + 4e = 2800
\n" ); document.write( "2d + 2s + 1e = 2200
\n" ); document.write( "---------------------subtraction eliminates d and s, find e
\n" ); document.write( "0d + 0s + 3e = 600
\n" ); document.write( "e = \"600%2F3\"
\n" ); document.write( "e = 200 cheap radios
\n" ); document.write( ":
\n" ); document.write( "Using the first two equations, replace e with 200
\n" ); document.write( "2d + 2s + 200 = 2200
\n" ); document.write( "2d + 2s = 2200 - 200
\n" ); document.write( "2d + 2s = 2000
\n" ); document.write( "and
\n" ); document.write( "7d + 3s + 2(200) = 3400
\n" ); document.write( "7d + 3s = 3400 = 400
\n" ); document.write( "7d + 3s = 3000
\n" ); document.write( ":
\n" ); document.write( "Multiply the above equation by 2, the 1st two unknown equation by 3
\n" ); document.write( "14d + 6s = 6000
\n" ); document.write( "6d + 6s = 6000
\n" ); document.write( "-----------------Subtraction eliminates s, find d
\n" ); document.write( "8d = 0; this means that there will be no deluxe radios
\n" ); document.write( ":
\n" ); document.write( "Find s using the 1st equation: 2d + 2s + 1e = 2200;
\n" ); document.write( "2(0) + 2s + 200 = 2200
\n" ); document.write( "2s = 2200 - 200
\n" ); document.write( "2s = 2000
\n" ); document.write( "s = \"2000%2F2\"
\n" ); document.write( "s = 1000 standard radios
\n" ); document.write( ":
\n" ); document.write( "I'm going to say the in order to use all the available transistors, you have
\n" ); document.write( "0 deluxe radios
\n" ); document.write( "1000 standard radios
\n" ); document.write( "200 cheap radios
\n" ); document.write( ":
\n" ); document.write( "This checks out in all three equations. \n" ); document.write( "
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