First we define the variables:
m = multiple choice questions
s = short answer questions
Next we need to satisfy 2 conditions:
1) There are a total of 40 questions. We can represent this mathematically using the variables I defined:
2) The multiple-choice questions are worth 2 points and the short-answer are worth 4 points but they need to total 100 points. This can also be represented mathematically:
By satisfying the conditions provided we were able to create the 2 equations!
Answer:
A
Step-by-step explanation:
Difference of squares: (a^2 - b^2) = (a - b)(a + b)
(144x^2 - 49) = (12x - 7) (12x + 7)
Answer:
55
Step-by-step explanation:
This is 55 because you need to make a sum of 180 when making a line and 125+55=180
Answer:
Step-by-step explanation:
Time taken in each lap = 4 min
Total laps = 11
Total time = 11 x 4 = 44min
Answer: 46 years
Step-by-step explanation:
Let the father's age be x and the son's age be y, then 3 years ago:
Father = x - 3
son = y - 3
Then , from the first statement :
x - 3 = 3 ( y - 3 )
x - 3 = 3y - 9
x = 3y - 9 + 3
x = 3y - 6 .......................................... equation 1
In five years time
father = x + 5
son = y + 5
Then , from the second statement
x + 5 = 2 ( y + 5 )
x + 5 = 2y + 10
x = 2y + 10 - 5
x = 2y + 5 ........................ equation 2
Equating equation 1 and 2 , we have
3y -6 = 2y + 5
add 6 to both sides
3y = 2y + 5 + 6
subtract 2y from both sides
3y - 2y = 11
y = 11
substitute y = 11 into equation 1 to find the value of x
x = 3y - 6
x = 3(11) - 6
x = 33 - 6
x = 27
This means that the father is presently 27 years and the son is presently 11 years.
In four years time
father = 27 + 4 = 31
son = 11 + 4 = 15
sum of their ages in four years time will be
31 + 15 = 46 years
