Question

My friend Elentine bought 2 kents and 6 dubbles for a total cost of $22.
My friend Boondin bought 9 kents and 4 dubbles for a total cost of $53.
Here are equations showing the relationship between cost of kents (x)
and cost of dubbles (y):
2x + y = 22
9x + 4y = 53
What were the prices for kents and dubbles?
$6 per kent, $2 per dubble
$2 per kent, $5 per dubble
$5 per kent, $2 per dubble
$2 per kent, $6 per dubble

Answer 1

The cost of one kent is $ 5

The cost of one dubbles is $ 2

Solution:

Let "x" be the cost of one kent

Let "y" be the cost of one dubbles

Elentine bought 2 kents and 6 dubbles for a total cost of $22

Therefore,

2x + 6y = 22

Reduce,

x + 3y = 11

x = 11 - 3y ------- eqn 1

Boondin bought 9 kents and 4 dubbles for a total cost of $53

9x + 4y = 53 ---------- eqn 2

Substitute eqn 1 in eqn 2

9(11 - 3y) + 4y = 53

99 - 27y + 4y = 53

23y = 46

Divide both sides by 23

y = 2

Substitute y = 2 in eqn 1

x = 11 - 3(2)

x = 11 - 6

x = 5

Thus the solution is (5, 2)