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 cornx + 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 equation2x + 250 = 420 Combine like terms2x = 170 Subtract 250 from both sidesx = 85 There are 85 acres of pumpkins420 – 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 Ounces of each bottle of perfume$15A + $35B = $63 The prices of each bottle to make the new bottle

A = 3 – B Isolate one of the values15(3-B) + 35B = 63 Substitute the value of A for A45 – 15B + 35B = 63 Distribute the 1545 + 20B =63 Combine like terms20B = 18 Subtract 45 from both sidesB = .9 Divide both sides by 20A + .9 = 3 Substitute .9 for BA = 2.1 Subtract .9 from both sides

Final Answer 2.1 of Perfume A .9 of Perfume B

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