1. Let S be the number of scientific calculators, G be the number of graphing calculators. S + G = 44 (the store bought 44 calculators) 11S + 53G = 1660 (the total purchase was $1660) Multiply the first equation by 11 and subtract from the second (11S+53G) - 11(S+G) = (1660) - 11(44) 42G = 1176 G = 1176/42 = 28 S = 44-28 = 16 The store ordered 16 scientific and 28 graphing calculators. 2. Use the elimination methd .3x - .2y = 4 .2x + .3y = -23/19 Multiply the first equation by 3 and add to 2 times the second equation. This will eliminate y. 3(.3x-.2y) + 2(.2x+.3y) = 3(4) + 2(-23/19) .9x + .4x = 12 - 46/19 1.3x = (228-46)/19 x = 182/(19*1.3) ≈ 7.3684 y = (.3x-4)/.2 = 1.5x-20 ≈ 1.5(7.3684)-20 = -8.9474 3. Use the elimination method .05x + .25y = 66 .15x + .05y = 72 Multiply the first equation by 3 and subtract the second. This will eliminate x. 3(.05x+.25y) - (.15x+.05y) = 3(66) - 72 .75y - .05y = 198-72 y = 126/.70 = 180 x = (66-.25y)/.05 = 21/.05 = 420 Check: .15(420)+.05(180) = 63+9 = 72 4. P = 190 = 2(w+(w+29)) 95 = 2w + 29 66 = 2w 33 inches = width 62 inches = length