Question

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?

Answer 1

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