Report

SYSTEMS of EQUATIONS WORD PROBLEMS A farmer grows only pumpkins and corn on her 420-acre farm. This year she wants to plant 250 more acres of corn than pumpkins. How many acres of each crop should the farmer plant? • Let x = pumpkins • Let y = corn • Group acres with acres and crops with crops x + y = 420 The number of acres for pumpkins and the acres for corn x + 250 = y There are 250 more acres of corn than there are pumpkins x+ x + 250 = 420 substitute x + 250 for y in the first equation 2x + 250 = 420 Combine like terms 2x = 170 Subtract 250 from both sides x = 85 There are 85 acres of pumpkins 420 – 85 There are 335 acres of corn A perfume maker has stocks of two perfumes on hand. Perfume A sells for $15 per ounce. Perfume B sells for $35 per ounce. How much of each should be combined to make a 3-oz bottle of perfume that can be sold for $63. A+B=3 $15A + $35B = $63 Ounces of each bottle of perfume The prices of each bottle to make the new bottle A=3–B 15(3-B) + 35B = 63 45 – 15B + 35B = 63 45 + 20B =63 20B = 18 B = .9 A + .9 = 3 A = 2.1 Isolate one of the values Substitute the value of A for A Distribute the 15 Combine like terms Subtract 45 from both sides Divide both sides by 20 Substitute .9 for B Subtract .9 from both sides Final Answer 2.1 of Perfume A .9 of Perfume B YOUR TURN