Answer:
The florist can make 11 regular bouquets and 21 mini bouquets
Step-by-step explanation:
The number of roses the florist has = 118 roses
The number of peonies the florist has = 226 peonies
The number of roses in each regular bouquet = 5 roses
The number of peonies in each regular bouquet = 11 peonies
The number of roses in each mini bouquet = 3 roses
The number of peonies in each mini bouquet = 5 peonies
1. The equation that gives the total number of roses to be used in both kinds of bouquet is given as follows;
Let r represent the number of regular bouquet the florist can make and let m represent the number of mini bouquet the florist can make, we have;
5·r + 3·m = 118...(1)
2. Similarly, we have;
11·r + 5·m = 226...(2)
Making m the subject of the formula of both equations, and equating both values of m to find a common solution, we have;
m = (118 - 5·r)/3
m = (226 - 11·r)/5
(118 - 5·r)/3 = (226 - 11·r)/5
5 × (118 - 5·r) = 3 × (226 - 11·r)
590 - 25·r = 678 - 33·r
33·r - 25·r = 678 - 590 = 88
8·r = 88
r = 88/8 = 11
r = 11
The number of regular bouquet the florist can make = r = 11
m = (118 - 5·r)/3 = (118 - 5×11)/3 = 21
m = 21
The number of mini bouquet the florist can make = m = 21
The number of regular bouquet the florist can make = 11 bouquets
The number of mini bouquet the florist can make = 21 bouquets.
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