4 apples and 3 pears=£2.70 2 apples and 5 pears =£2.40 how much does 1 apple cost and 1 pear

Question

asked Jun 18, 2023 218k views

2 Answers

Cross Vander · Answer 1 · 2023-06-22T02:59:45+0000

Answer:

Cost of each apple:
0.45 .

Cost of each pear:
0.30 .

Explanation:

Let
denote the cost of each apple. Let
denote the cost of each pear.

The question states that the cost of
apples and
pears is
2.70 . Thus:

$4\, x + 3\, y = 2.70$ .

Likewise, since the cost of
apples and
pears is
2.40 :

$2\, x + 5\, y = 2.40$ .

Solve this system of equations for
and
to find the price of each fruit.

$\left\lbrace \begin{aligned} & 4\, x + 3\, y = 2.70 \\ & 2\, x + 5\, y = 2.40\end{aligned}\right.$ .

Multiply both sides of the equation
$2\, x + 5\, y = 2.40$ by
to match the coefficient of
in the first equation:

$\left\lbrace \begin{aligned} & 4\, x + 3\, y = 2.70 \\ & (2* 2)\, x + (2 * 5)\, y = (2 * 2.40)\end{aligned}\right.$ .

$\left\lbrace \begin{aligned} & 4\, x + 3\, y = 2.70 \\ & 4\, x + 10\, y = 4.80 \end{aligned}\right.$ .

Substitute the first equation from the new equation to eliminate
and solve for
:

$\begin{aligned}& 4\, x + 10\, y - (4\, x +3\, y) = 4.80 - 2.70\end{aligned}$ .

$10\, y - 3\, y = 2.10$ .

$7\, y = 2.10$ .

y = 0.30 .

Substitute
y = 0.30 into an equation from the original system to eliminate
and solve for
.

$2\, x + 5\, y = 2.40$ .

$2\, x + 5 * 0.30 = 2.40$ .

$2\, x = 0.90$ .

x = 0.45 .

Thus,
x = 0.45 and
y = 0.30 .

In other words, the price of each apple would be
0.45 . The price of each pear would be
0.30 .