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
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