Answer:
(a) 5 mayflies
(b) 15 mayflies
(c) 84 flying flies
Step-by-step explanation:
Represent Mayflies with M and the total flying insects with F
The ratio can be represented as:
![M : F = 5 : 14](https://tex.z-dn.net/?f=M%20%3A%20F%20%3D%205%20%3A%2014)
Solving (a):
![F = 14](https://tex.z-dn.net/?f=F%20%3D%2014)
Find M
Substitute 14 for F in ![M : F = 5 : 14](https://tex.z-dn.net/?f=M%20%3A%20F%20%3D%205%20%3A%2014)
![M : 14 = 5 : 14](https://tex.z-dn.net/?f=M%20%3A%2014%20%3D%205%20%3A%2014)
Convert to fraction
![\frac{M}{14} = \frac{5}{14}](https://tex.z-dn.net/?f=%5Cfrac%7BM%7D%7B14%7D%20%3D%20%5Cfrac%7B5%7D%7B14%7D)
Multiply through by 14
![14 * \frac{M}{14} = \frac{5}{14} * 14](https://tex.z-dn.net/?f=14%20%2A%20%5Cfrac%7BM%7D%7B14%7D%20%3D%20%5Cfrac%7B5%7D%7B14%7D%20%2A%2014)
![M = 5](https://tex.z-dn.net/?f=M%20%3D%205)
Solving (b):
![F = 42](https://tex.z-dn.net/?f=F%20%3D%2042)
Find M
Substitute 42 for F in ![M : F = 5 : 14](https://tex.z-dn.net/?f=M%20%3A%20F%20%3D%205%20%3A%2014)
![M : 42 = 5 : 14](https://tex.z-dn.net/?f=M%20%3A%2042%20%3D%205%20%3A%2014)
Convert to fraction
![\frac{M}{42} = \frac{5}{14}](https://tex.z-dn.net/?f=%5Cfrac%7BM%7D%7B42%7D%20%3D%20%5Cfrac%7B5%7D%7B14%7D)
Multiply through by 42
![42 * \frac{M}{42} = \frac{5}{14} * 42](https://tex.z-dn.net/?f=42%20%2A%20%5Cfrac%7BM%7D%7B42%7D%20%3D%20%5Cfrac%7B5%7D%7B14%7D%20%2A%2042)
![M = \frac{5}{14} * 42](https://tex.z-dn.net/?f=M%20%3D%20%5Cfrac%7B5%7D%7B14%7D%20%2A%2042)
![M=5*3](https://tex.z-dn.net/?f=M%3D5%2A3)
![M= 15](https://tex.z-dn.net/?f=M%3D%2015)
Solving (c):
![M = 30](https://tex.z-dn.net/?f=M%20%3D%2030)
Find F
Substitute 30 for M in ![M : F = 5 : 14](https://tex.z-dn.net/?f=M%20%3A%20F%20%3D%205%20%3A%2014)
![30 : F = 5 : 14](https://tex.z-dn.net/?f=30%20%3A%20F%20%3D%205%20%3A%2014)
Convert to fraction
![\frac{F}{30} = \frac{14}{5}](https://tex.z-dn.net/?f=%5Cfrac%7BF%7D%7B30%7D%20%3D%20%5Cfrac%7B14%7D%7B5%7D)
Multiply through by 30
![30 * \frac{F}{30} = \frac{14}{5} * 30](https://tex.z-dn.net/?f=30%20%2A%20%5Cfrac%7BF%7D%7B30%7D%20%3D%20%5Cfrac%7B14%7D%7B5%7D%20%2A%2030)
![F = \frac{14}{5} * 30](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7B14%7D%7B5%7D%20%2A%2030)
![F = 14*6](https://tex.z-dn.net/?f=F%20%3D%2014%2A6)
![F = 84](https://tex.z-dn.net/?f=F%20%3D%2084)
length of fabric =3 yards
width of fabric =1 1/3 =4/3 yards
Area =length * width
Area = 3 *4/3
Area =4 yards square
Step-by-step explanation:
15t + 30 = 20t | -15t
30 = 5t
t = 30/5 = 6
20 + 5t = -6t + 86 | + 6t
20 + 11t = 86 | -20
11t = 66
t = 6
18t + 20 = 24t + 50 | -18t
20 = 6t + 50 | -50
-30 = 6t
t = -30/6 = -5
18t - 2 = 10t + 54 | -10t
8t - 2 = 54 | +2
8t = 56
t = 56/8 = 7
7t - 5 = 15t + 91 | -7t
-5 = 8t + 91 | -91
-96 = 8t
t = -96/8 = -12
Answer: D
Step-by-step explanation: