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A store sells lemons and oranges. 3 lemons and 2 oranges weigh 200g. 4 lemons and 4 oranges weigh 300g. Find the weight of one lemon and one orange.

Mathematics

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Answers

2 parts
a

\begin{align} 3x + 2y &= 200 \\ 4x + 4y &= 300 \end{align}

b

Lemon: 50 grams, Orange: 25 grams\text{Lemon: } 50 \text{ grams, Orange: } 25 \text{ grams}

Step-by-step solution

4 steps

Part a

Let xx be the weight of a lemon in grams.
Let yy be the weight of an orange in grams.

From the first statement, "3 lemons and 2 oranges weigh 200 grams":

3x+2y=2003x + 2y = 200

From the second statement, "4 lemons and 4 oranges weigh 300 grams":

4x+4y=3004x + 4y = 300

The two mathematical equations are:

3x+2y=2004x+4y=300\boxed{\begin{align*} 3x + 2y &= 200 \\ 4x + 4y &= 300 \end{align*}}

Part b

Lemon: 50 grams, Orange: 25 grams\text{Lemon: } 50 \text{ grams, Orange: } 25 \text{ grams}

  1. Write down the system of equations.

    3x+2y=200(1)3x + 2y = 200 \quad (1) 4x+4y=300(2)4x + 4y = 300 \quad (2)

  2. Simplify equation (2) by dividing by 2.

    4x2+4y2=3002\frac{4x}{2} + \frac{4y}{2} = \frac{300}{2} 2x+2y=150(3)2x + 2y = 150 \quad (3)

  3. Subtract equation (3) from equation (1) to eliminate yy.

    (3x+2y)−(2x+2y)=200−150(3x + 2y) - (2x + 2y) = 200 - 150 3x−2x+2y−2y=503x - 2x + 2y - 2y = 50 x=50x = 50

  4. Substitute the value of xx into equation (3) to find yy.

    2(50)+2y=1502(50) + 2y = 150 100+2y=150100 + 2y = 150 2y=150−1002y = 150 - 100 2y=502y = 50 y=502y = \frac{50}{2} y=25y = 25

    The weight of a lemon is 50 grams and the weight of an orange is 25 grams.

    Lemon: 50 grams, Orange: 25 grams\boxed{\text{Lemon: } 50 \text{ grams, Orange: } 25 \text{ grams}}
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