Tina has some ants and worms. There are 20 more ants than worms. Altogether, there are 80 insects. Let a represent the number of ants and w represent the number of worms. The following system of equations represents this situation: a−20=w a+w=80 How many ants and worms does Tina have?

a = number of ants
w = number of worms

There are 20 more ants than worms.
 ⇒ a - 20 = w

There are 80 insects.
⇒ a + w = 80

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Solve for a and w :
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a -20 = w -------------- (1)
a + w = 80 -------------- (2)

Substitute equation (1) into (2) :
a + (a - 20) = 80
a + a - 20 = 80  
2a - 20 = 80             // combine like terms
2a = 100                  // add 20 to both sides
a = 50                      // divide by 2 on both sides

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Sub a = 30 into equation (1) :
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a - 20 = w
50 - 20 = w
 w = 30

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Find ants and worms :
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ants = a = 50
worms = w = 30

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Answer: There are 50 ants and 30 worms.
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