Answer:
60 students passed, and 75 appeared in examination.
Step-by-step explanation:
Let's say s is the total number of students and p is the number of students who passed.
80% of the students passed, so:
0.8 s = p
If there were 10 less passers, and 15 less students (5 less failures), then the ratio of passers to failures would be 5/1.
(p − 10) / (s − p − 5) = 5 / 1
Simplify the second equation:
p − 10 = 5 (s − p − 5)
p − 10 = 5s − 5p − 25
6p = 5s − 15
Substitute the first equation.
6 (0.8 s) = 5s − 15
4.8 s = 5s − 15
0.2 s = 15
s = 75
p = 0.8 s
p = 60
60 students passed, and 75 appeared in examination.
A/2-b/3=1 solve for a, add b/3 to both sides
a/2=1+b/3 which is equal to
a/2=(3+b)/3 multiply both sides by 2
a=(6+2b)/3 now you can substitute this into 2a+3b giving you:
2(6+2b)/3 + 3b which is equal to
(12+4b+9b)/3
(13b+12)/3
Answer: the cost of each bush is $15
the cost of each flower is $2
Step-by-step explanation:
Let x represent the cost of each bush.
Let y represent the cost of each flower.
Portia bought 12 bushes and 30 flowers for $240 to plant in her yard. This is expressed as
12x + 30y = 240- - - - - - - - - - -1
Later, she realized she did not have enough plants and bought 7 more bushes and 10 more flowers for $125. This is expressed as
7x + 10y = 125- - - - - - - - - - -2
Multiplying equation 1 by 7 and equation 2 by 12, it becomes
84x + 210y = 1680
84x + 120y = 1500
Subtracting, it becomes
90y = 180
y = 180/90
y = 2
Substituting y = 2 into equation 1, it becomes
12x + 30 × 2 = 240
12x + 60 = 240
12x = 240 - 60 = 180
x = 180/12
x = 15
The standard compound interest formula is
Future value after x years with an annual interest of i
=Present Value (1+i)^x [which is an exponential function]
for given present value of $360. interest=0.03 (3%) and a total of x years, above equation reduces to
Future value after x years
=360(1.03^x)
