CaraRose1887
01.12.2020 •
Mathematics
PLEASE HELP I DON'T UNDERSTAND! A florist is making regular bouquets and mini bouquets. The florist has 118 roses and 226 peonies to use in the bouquets. Each regular bouquet has 5 roses and 11 peonies. Each mini bouquet has 3 roses and 5 peonies. Reply to this post by doing the following: 1. Write an equation that shows the total number of roses to be used in both kinds of bouquets. 2. Write an equation that shows the total number of peonies to be used in both kinds of bouquets. 3. Find how many of each bouquet can the florist make.
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Ответ:
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.
Ответ:
The area of the shaded region is 38.50 square units
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
The area of the shaded region is equal to the area of triangle ABE plus the area of triangle CDE
Remember that the area of triangle is equal to
where
b is the base
h is the height
Find the area of triangle ABE
substitute the values
Find the area of triangle CDE
substitute the values
Find the area of the shaded region