MATH SOLVE

9 months ago

Q:
# one week, the music store sold 2 trumpets, 3 clarinets, and 5 violins for $1240. the next week, they sold 3 trumpets, 1 clarinet, and 4 violins for $1027. the following week, they sold 5 trumpets, 7 clarinets, and 2 violins for $2091. find the cost of a trumpet, a clarinet would, and a violin.

Accepted Solution

A:

One week, the music store sold 2 trumpets, 3 clarinets, and 5 violins for $1240. the next week, they sold 3 trumpets, 1 clarinet, and 4 violins for $1027. the following week, they sold 5 trumpets, 7 clarinets, and 2 violins for $2091.Let x be the cost of trumpets y be the cost of clarinetsz be the cost of violinsNow we frame equations2x +3y + 5z = 1240 ---> equation 13x + 1y + 4z = 1027---> equation 25x + 7y + 2z = 2091 ---> equation 3Now we solve for x,y and z using elimination methodMultiply the second equation by -3 and with first equation2x +3y + 5z = 1240 -9x - 3y -12z = -3081---------------------------------7x - 7z = -1841 ( divide both sides by -7) x + y = 263 ----------> equation 4Multiply the second equation by -7 and add it with third equation-21x - 7y - 28z = -7189 5x + 7y + 2z = 2091 -------------------------------------16x - 26z = -5098 (divide the whole equation by -2)8x + 13z = 2549 --------> equation 5Now use equation 4 and 5 to eliminate x. Multiply equation 4 by 8-8x - 8z = -2104
8x + 13z = 2549------------------------------5z = 445z = 89We know x + z = 263, replace z with 89x + 89 = 263 ( subtract 89 on both sides)x = 1742x +3y + 5z = 1240 ---> equation 1 ( substitute the values of x and z)2(174) + 3y + 5(89) = 1240348 + 3y + 445 = 1240793 + 3y = 1240 ( subtract 793 on both sides)3y = 447 ( divide by 3 on both sides)y = 149The cost of trumpets = $174The cost of clarinets = $149The cost of violins = $89