Derek wants to order some roses online. Florist A charges $4.75 per blue rose plus $40 delivery charge. Florist B charges $5.15 per red rose plus $25
delivery charge. If Florist B increases the cost per rose to $5.20, for what
number of roses is it less expensive to order from Florist A? From Florist B?

Step-by-step explanation:

let the total charge be y

and the number of rose be x

Florist A charges

y=40+4.75x1

Florist B charges

y=25+5.2x2

to solve for the number of roses we need to equate 1 and 2

40+4.75x=25+5.2x

40-25=5.2x-4.75x

15=0.45x

x=15/0.45

x=33.33

The number of roses that will be less expensive to order from A is 33.33

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)