Question
The sum of 5 times the width of a rectangle and twice its length is 26 units. The Difference of 15times the width and three times the length is 6
units . Write and Solve a system of equations to find the length and width of the rectangle.
Hint:
Frame the equations and then solve.
The correct answer is: We can also solve these system of equations by making the coefficients of to be the same in both the equations
Complete step by step solution:
Let's denote the width of the rectangle = w
and denote the length of the rectangle = l
Let 5w 2l = 26…(i)
and 15w - 3l = 6….(ii)
On multiplying (i) with 3, we get 3( 5w + 2l = 26)
⇒15w + 6l =78…(iii)
Now, we have the coefficients of w in (ii) and (iii) to be the same.
On subtracting (ii) from (iii),
we get LHS to be 15w + 6l - (15w - 3l) = 6l + 3l = 9l
and RHS to be 78 - 6 = 72
On equating LHS and RHS, we have 9l =72
⇒ l = 8
On substituting the value of l in (i), we get 5w + 2 × 8 = 26
⇒ 5w + 16 = 26
⇒ 5w = 26-16
⇒ 5w = 10
⇒ w = 2
Hence we get w = 2 and l = 8
Note: We can also solve these system of equations by making the coefficients of
to be the same in both the equations
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Tips to help you answer the questions on the problems of age: a.) The age after n years will be (x+n) if you assume that the current age is x.
b.) The age before n years will be (x-n) if you assume the present age to be x.
c.) If the age is expressed as a ratio, p:q, the age will be rounded to the nearest multiple of q and p.
d.) Given that you are assuming you are currently x years old, n times that number equals (xn) years.
E.g.:The father is three times older than Ronit. So he would be 2.5 times Ronit's age after '8' years. How many more times would he be Ronit's age after another '8' years?
A. 2 times
B. 2 1/2 times
C. 2 3/4 times
D. 3 times
Richard and teo have a combined age of 31 . Richard is 4 years older than twice teo's age. How old are Richard and teo?
Tips to help you answer the questions on the problems of age: a.) The age after n years will be (x+n) if you assume that the current age is x.
b.) The age before n years will be (x-n) if you assume the present age to be x.
c.) If the age is expressed as a ratio, p:q, the age will be rounded to the nearest multiple of q and p.
d.) Given that you are assuming you are currently x years old, n times that number equals (xn) years.
E.g.:The father is three times older than Ronit. So he would be 2.5 times Ronit's age after '8' years. How many more times would he be Ronit's age after another '8' years?
A. 2 times
B. 2 1/2 times
C. 2 3/4 times
D. 3 times
