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Braden and Jason, who are florists, purchased flower bouquets and vases at the same store. Braden bought 3 flower bouquets and 5 vases for a total of $25.75. Jason bought 8 flower bouquets and 2 vases for a total of $29.00. What is the price of a flower bouquet?

User Gregtzar
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1 Answer

3 votes
Let flower bouquet be
f and vase be
v

Form two equations as follow


3f+5v=25.75 ---> Equation 1

8f+2v=29 ----> Equation 2

Using the elimination method:

Choose which variable, either
f or
v that we want to eliminate first. Say we choose
v

The next step is we need to make the constants of
v to be the same value. At the moment we have
5v and
2v. Using the concept of common multiple, we will multiply
5v by
2 and the
2v by 5 to get both
v's with a constant 10

The rule of the Algebraic equation is: if we multiply one term by
k, then we need to do the same with all the other terms in the equations. So now we have

(
3f+5v=25.75)×2 ⇒
6f+10v=51.5
(
8f+2v=29)×5⇒
40f+10v=145

Now we can eliminate
v by subtracting Equation 1 from Equation 2 (it would also work the other way around)

Equation 2 - Equation 1

40f-6f+10v-10v=145-51.5

34f=93.5

f=2.75

Now we've worked out the price of one flower bouquet, we can substitute back
f=2.75 into either equation 1 or equation 2 to work out the price of one vase


3(2.75)+5v=25.75

5v=25.75-8.25

5v=17.5

v=3.5

Hence, the price of one bouquet is $2.75 and one vase is $3.50
User Suzette
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