The price of 4 citrons and 5 fragrant wood apples is 46 units. The price of 5 citrons and 4 fragrant wood apples is 53 units. Find the price of a citron and the price of a wood apple.
4c + 5a = 46
5c + 4a = 53
Multiply first equation by 5 and second by 4.
20c + 25a = 230
20c + 16a = 212
Subtract second equation from first to solve for a. Insert that value into either of first two equations to solve for c.
To solve this problem, let's assign variables to the unknown prices. Let the price of a citron be 'c' and the price of a fragrant wood apple be 'w'.
From the given information, we can set up two equations:
Equation 1: 4c + 5w = 46
Equation 2: 5c + 4w = 53
We have a system of two equations with two variables. We can solve this system using the method of substitution or elimination.
Let's use the method of elimination to solve the system:
Multiply equation 1 by 5 and equation 2 by 4 to make the coefficients of 'c' or 'w' equal.
5 * (4c + 5w) = 5 * 46 simplifies to 20c + 25w = 230
4 * (5c + 4w) = 4 * 53 simplifies to 20c + 16w = 212
Now, subtract equation 2 from equation 1:
(20c + 25w) - (20c + 16w) = 230 - 212
Simplifying further, we get:
20c - 20c + 25w - 16w = 18
9w = 18
Divide both sides by 9:
w = 18 / 9
w = 2
Now substitute the value of 'w' back into one of the original equations (let's use equation 1):
4c + 5w = 46
4c + 5(2) = 46
4c + 10 = 46
4c = 46 - 10
4c = 36
Divide both sides by 4:
c = 36 / 4
c = 9
Therefore, the price of a citron is 9 units and the price of a fragrant wood apple is 2 units.
To solve this problem, we can set up a system of equations based on the given information.
Let's assume the price of one citron is "c" units and the price of one fragrant wood apple is "w" units.
According to the first statement, the price of 4 citrons and 5 fragrant wood apples is 46 units. So, we can write the equation as:
4c + 5w = 46 ----(1)
According to the second statement, the price of 5 citrons and 4 fragrant wood apples is 53 units. So, we can write the equation as:
5c + 4w = 53 ----(2)
Now, we have a system of two equations with two variables. We can solve it using various methods, but here we will use the method of elimination.
Multiply equation (1) by 4 and equation (2) by 5 to eliminate the "w" term:
(4 * 4c) + (4 * 5w) = (4 * 46)
(5 * 5c) + (5 * 4w) = (5 * 53)
Which simplifies to:
16c + 20w = 184 ----(3)
25c + 20w = 265 ----(4)
Now, subtract equation (4) from equation (3) to eliminate the "w" term:
(16c + 20w) - (25c + 20w) = 184 - 265
16c - 25c = -81
Simplifying further:
-9c = -81
Divide both sides by -9:
c = -81 / -9
c = 9
Now, substitute the value of c back into equation (1) or (2) to find the value of w.
Using equation (1):
4c + 5w = 46
4(9) + 5w = 46
36 + 5w = 46
5w = 46 - 36
5w = 10
w = 10 / 5
w = 2
Therefore, the price of a citron is 9 units, and the price of a fragrant wood apple is 2 units.
4 c + 5 a = 46
5 c + 4 a = 53
multiply first equation by 5 and second by 4
20 c + 25 a = 230
20 c + 16 a = 212
--------------------------- subtract
9 a = 18
a = 2 units per apple
then back to
4 c + 5 a = 46
4 c + 10 = 46
c = 36/4 = 9 units per lemon