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?
----------------------------------- Solve for a and w : ----------------------------------- 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
----------------------------------- Sub a = 30 into equation (1) : ----------------------------------- a - 20 = w 50 - 20 = w w = 30
----------------------------------- Find ants and worms : ----------------------------------- ants = a = 50 worms = w = 30
---------------------------------------------------------------------- Answer: There are 50 ants and 30 worms. ----------------------------------------------------------------------
