Question

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

Answer 1

Answer:

Cost of each apple: $0.45$.

Cost of each pear: $0.30$.

Step-by-step explanation:

Let $x$ denote the cost of each apple. Let $y$ denote the cost of each pear.

The question states that the cost of $4$ apples and $3$ pears is $2.70$. Thus:

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

Likewise, since the cost of $2$ apples and $5$ pears is $2.40$:

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

Solve this system of equations for $x$ and $y$ 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 $2$ to match the coefficient of $x$ in the first equation:

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

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

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

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

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

$7\, y = 2.10$.

$y = 0.30$.

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

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

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

$2\, x = 0.90$.

$x = 0.45$.

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 $0.30$.

Answer 2

Answer:

The answer is 0.45 pounds for an apple and 0.3 pounds for a pear

Step-by-step explanation: