Question

In 1 month 12 gloves were sold for a total of $561. Right handed des gloves cost $45 and left handed gloves cost 52$ each. How many of each type of glove were sold

Answer 1

9 right handed gloves and 3 left handed gloves were sold

Solution:

Let "x" be the number of right handed gloves sold

Let "y" be the number of left handed gloves sold

Cost of 1 right handed gloves = $ 45

Cost of 1 left handed gloves = $ 52

1 month 12 gloves were sold for a total of $561

So 12 gloves are sold

Therefore, frame a equation as,

number of right handed gloves sold + number of left handed gloves sold = 12

x + y = 12 -------- eqn 1

They were sold for a total of $ 561

number of right handed gloves sold x Cost of 1 right handed gloves + number of left handed gloves sold x Cost of 1 left handed gloves = 561

$x \times 45 + y \times 52 = 561$

45x + 52y = 561 --------- eqn 2

Let us solve eqn 1 and eqn 2

From eqn 1,

x = 12 - y ------------ eqn 3

Substitute eqn 3 in eqn 2

45(12 - y) + 52y = 561

540 - 45y + 52y = 561

7y = 561 - 540

7y = 21

y = 3

Substitute y = 3 in eqn 3

x = 12 - 3

x = 9

Thus 9 right handed gloves and 3 left handed gloves were sold