Literal Equations
and Formulas
Common Core State Standards
A-CED.A.4 Rearrange formulas to highlight a quantity
of interest, using the same reasoning as in solving
equations... Also A-CED.A.1, A-REI.A.1
MP 1, MP 2, MP 3, MP 4, MP 8Objective To rew rite an d use literal eq u atio n s a n d form ulasGetting Ready!You a re ordering pizzas and sandwiches.
You have a budget o f $ 8 0. How many
sandwiches can you buy if you buyWhat happens to (^) 4 pizzas? 5 pizzas? Explain your answer.
the number of
sandwiches as th e
number of pizzas
increases?
mat hemat ical In t^ s lesson> You W>U learn to solve p roblem s using eq u atio n s in m ore th a n
PRACTICES one variable. A literal equation is an eq u a tio n th a t involves two or m ore variables.
Esse n t i a l U n d e r st a n d i n g W hen you w ork w ith literal equations, you can use
th e m eth o d s you have learn ed in this ch a p te r to isolate any particu lar variable.
Lesson
Vocabulary
literal equation
formula
Why should you
rewrite the equation?
If you re w rite th e
equation, you have to
isolate y only once. Then
s u b s titu te fo r x. If you
s u b s titu te fo r x firs t,
you must is o la te /tw ic e
(once fo r each x-value).
Rewriting a Literal Equation
The equation lOx + 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 th e eq u a tio n lOx + 5y = 80 fory.
lOx + 5y = 80
lOx + 5y - lOx = 80 - lOx Subtract 10x fro m each side.
5y = 80 - lOx Simplify.
ty = 8 0 - lO x Divide each sjde by 5
y = 16 - 2x Simplify.
Step 2 Use th e rew ritten eq u a tio n to find y w h en x = 3 a n d w h e n x = 6.
y = 16 - 2x y = 16 - 2x
y = 16 - 2(3) Substitute forx. y = 16 - 2(6)
y = 10 Simplify. y = 4
If you buy 3 pizzas, you can buy 10 sandw iches. If you buy 6 pizzas, you can buy
4 sandw iches.
c
PowerAlgebra.com | Lesso n 2- 5 Li t er al Eq u at i o n s an d Fo rm u las^109