Question

A rental truck company plans to spend $13 million on 320 new vehicles. Each commercial van will cost $25,000, each small truck $50,000, and each large truck $80,000. Past experience shows that they need twice as many vans as small trucks. How many of each type of vehicle can they buy? Write a linear system of equations. Let x be the number of vans, y be the number of small trucks, and z be the number of large trucks. Choose the correct answer below. O A. x+y+z = 320 25.000x + 50,000y + 80,000z = 13,000,000 x - 2y = 0 OC. X+ y + z = 560 25,000x + 50,000y = 13,000,000 x-2y = 320 O B. x + y + 2z = 320 25,000x + 50.000y + 80,000z = 13,000,000 x + 3y = 0 OD. 3x + y + z = 320 25.000x + 50.000y + 80.000z = 13.000.000 x - 2y + z = 0 They can buy Ivans, (Simplify your answers.) small trucks, and large trucks

Answer 1

Total amount to spend = $13 million Total No. of New vehicles = 320. het The number of vans an The number of small trucks=Y. The number of - + de Total No. of vehiches - sety +2=320 -0 Barge trucks = Z. Cost of one van = $25,000 So i'cost of re-vens = $25,000 again 3 so and so cost of cast of cost of rest of one- small truck = $50,000 y Small trucks=$50,00Y. one-Large truck = $80,000 2- lorge bucks = $80,002 So, the total cast is 2500ory 56,000 4 + 80, 2007 13 million. and it must be equal to 25,000 + 50,000y + 80,000Z = 13,000, ovo 2 the small again the no. of vans is twice then trick. Hence x=24 => x-2y = 0 - Hence the Linear system is :- x + y + z = 320.. 2 Sproxe + sooooo y + 80, OUD Z = 13,000,000 6 H-2y =0 J olotion-A

Now, we values of ny and z. Solque egn 0 1 multiplying ean 9 ve egno, o ando for the y ean o by 80,000 and then. 0-0 8 quo x 25000 2 * &quoy + Sauz = 25$oopoo soby + samoz 13,cmioro + 8gvoy + sau + soapy + sau - 0 again from subtracting 55,000n + 301 ovoy = 12,600,000 multiplying egn © by 55,000 and eh☺, we have 5 soron + 30, ovdy = 12,600, co 55,qoo x I 110, oooy = 0 140,000y = 12,600, OUD 4 144 = 1260 using this in ean@, we have 4290) 50 =1/x=180) using , the values of nay in ♡, we get 180+90+8= 320 = 270+2=320 => z= 329-270 =>3= 50/ Hence they can buy [180) reans, 190 small trucks and [50) large trucks,