Question

Solve this problem. A florist sells holiday bouquets that use roses and carnations in a ratio of 2 to 7. She receives a shipment of 343 carnations. How many roses will the florist need

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Answer 1

Let roses be R and carnations be C

"in a ratio of 2 to 7" means that the ratio of R to C is 2 to 7, meaning you'll have to cross multiply to translate it algebraically

`R:C\\2:7\\7R=2C\\`

since C = 343 we plug 343 in
`7R=2C`:

`7R=2(343)\\7R=686\\R=(686)/(7) \\R=98`

ergo, she needs 98 roses

to make sure of the answer:

"ratio of 2 to 7" is technically a fraction =>
`(2)/(7)`

and since the ratio of the roses to the carnations is the same as
`(2)/(7)` we plug the values R = 98 and C=343:

`(R)/(C)=(98)/(343)=(2)/(7)`

check with calculator too, hope i helped <33