Question

The price of 8 citrons and 3 fragrant wood apples is 48 units. The price of 3 citrons and 8 fragrant wood apples is 73 units. Find the price of a citron and the price of a wood apple.

a) Citron price: 3 units, Wood apple price: 7 units
b) Citron price: 5 units, Wood apple price: 6 units
c) Citron price: 4 units, Wood apple price: 9 units
d) Citron price: 2 units, Wood apple price: 10 units

Answer 1

By setting up a system of linear equations from the problem and either subtracting or substituting, we find that the price of a citron is 3 units and the price of a wood apple is 8 units, which corresponds to option a).

Step-by-step explanation:

To find the price of a citron and the price of a wood apple, we can set up a system of linear equations based on the information given:

1. For the first situation, the equation would be 8C + 3W = 48, where C is the price of a citron and W is the price of a wood apple.
2. For the second situation, the equation would be 3C + 8W = 73.

Now we will solve this system using the method of substitution or elimination to find the values of C and W.

Using Substitution or Elimination

Multiply the first equation by 3 and the second equation by 8 to make the coefficients of C equal:

• 24C + 9W = 144 (first equation multiplied by 3)
• 24C + 64W = 584 (second equation multiplied by 8)

Subtract the first new equation from the second new equation to eliminate C:

• 55W = 440 (subtracting the equations)

Divide by 55 to find the price of a wood apple:

• W = 440 / 55
• W = 8 units

Substitute W = 8 back into the first original equation:

• 8C + 3(8) = 48
• 8C + 24 = 48
• 8C = 24
• C = 24 / 8
• C = 3 units

Therefore, the price of a citron is 3 units and the price of a wood apple is 8 units.