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 $7R=2C$:

$7R=2(343)\\7R=686\\R=\frac{686}{7} \\R=98$

ergo, she needs 98 roses

to make sure of the answer:

"ratio of 2 to 7" is technically a fraction =>  $\frac{2}{7}$

and since the ratio of the roses to the carnations is the same as $\frac{2}{7}$ we plug the values R = 98 and C=343:

$\frac{R}{C}=\frac{98}{343}=\frac{2}{7}$

check with calculator too, hope i helped <33