Dynamic Activity

Solving Formulas for Any Variable

Lesson Vocabulary

• literal equation
• formula

Problem 1 Rewriting a Literal Equation

The equation 10x + 5y = 80, where x is the number of pizzas and y is the number of sandwiches, models the problem in the Solve It. How many sandwiches can you buy if you buy 3 pizzas? 6 pizzas?

• Step 1 Solve the equation 10x + 5y = 80 for y.

  10 x + 5 y = 80   10 x + 5 y − 10 x = 80 − 10 x Subtract  10 x  from each side . 5 y = 80 − 10 x Simplify . 5 y 5 = 80 − 10 x 5 Divide each side by  5 . y = 16 − 2 x Simplify . table with 5 rows and 3 columns , row1 column 1 , 10 x plus 5 y , column 2 equals 80 , column 3 , row2 column 1 , 10 x plus 5 y minus 10 x , column 2 equals 80 minus 10 x , column 3 cap subtract . 10 x . fromeachside . . , row3 column 1 , 5 y , column 2 equals 80 minus 10 x , column 3 cap simplify , . , row4 column 1 , fraction 5 y , over 5 end fraction , column 2 equals . fraction 80 minus 10 x , over 5 end fraction , column 3 cap divideeachsideby . 5 . , row5 column 1 , y , column 2 equals 16 minus 2 x , column 3 cap simplify , . , end table

• Step 2 Use the rewritten equation to find y when x = 3 and when x = 6.

  y = 16 − 2 x   y = 16 − 2 x y = 16 − 2 ( 3 ) Substitute for  x . y = 16 − 2 ( 6 ) y = 10 Simplify. y = 4 table with 3 rows and 3 columns , row1 column 1 , y equals 16 minus 2 x , column 2 , column 3 y equals 16 minus 2 x , row2 column 1 , y equals 16 minus 2 open 3 close , column 2 cap substitute for . x . , column 3 y equals 16 minus 2 open 6 close , row3 column 1 , y equals 10 , column 2 cap simplify. , column 3 y equals 4 , end table

If you buy 3 pizzas, you can buy 10 sandwiches. If you buy 6 pizzas, you can buy 4 sandwiches.