Linear Equations in Two Variables Test - 14

Money spent by Mark each day = $1.20

Thus, money spent by Mark in d days = d × $1.20 = $1.2d

Money with Mark at the start of the week = $15

Thus, money left with Mark after d days = $m = $15 − $1.2d

∴ m = 15 −1.2d

The correct answer is C.

Number of titles won in the 1^st year = 3 × 1 = 3

Number of titles won in the 2^nd year = 3 × 2 = 6

Number of titles won in the 3^rd year = 3 × 3 = 9

Number of titles won in the 4^th year = 3 × 4 = 12

Number of titles won in the 5^th year = 3 × 5 = 15

Thus, the rule followed in the given table is y = 3x

The correct answer is A.

The linear equation is y = 4x + 3

For: x = −2, y = 4(−2) + 3

= −8 + 3

= − 5

x = −1 y = 4(−1) + 3

= −4 + 3

= −1

x = 0 y = 4(0) + 3

= 0 + 3

= 3

x = 1 y = 4(1) + 3

= 4 + 3

= 7

The required table is:

The correct answer is A.

The number of books is Max’s library = 40

The number of books with Ben = z

According to the question, z − 5 = y + 5

⇒ z − 5 = 40 + 5

⇒ z = 45 + 5

⇒ z = 50

Therefore, the total number of books in both the libraries combined is

40 + 50 = 90

The correct answer is D.

The given two-digit number xy can be written as 10x + y.

When the digits are interchanged, the number 10y + x is obtained.

It is given that when the digits are interchanged, the number increases by 27.

∴ 10x + y + 27 = 10y + x

⇒ 9x − 9y + 27 = 0

⇒ 9(x − y + 3) = 0

Dividing both sides by 9, we get

x − y + 3 = 0

Thus, the required relationship is x − y + 3 = 0.

Hence, the correct answer is option D.