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
[tex]R:C\\2:7\\7R=2C\\[/tex]
since C = 343 we plug 343 in [tex]7R=2C[/tex]:
[tex]7R=2(343)\\7R=686\\R=\frac{686}{7} \\R=98[/tex]
ergo, she needs 98 roses
to make sure of the answer:
"ratio of 2 to 7" is technically a fraction => [tex]\frac{2}{7}[/tex]
and since the ratio of the roses to the carnations is the same as [tex]\frac{2}{7}[/tex] we plug the values R = 98 and C=343:
[tex]\frac{R}{C}=\frac{98}{343}=\frac{2}{7}[/tex]
check with calculator too, hope i helped <33
