A fruit company delivers it’s fruit and two types of boxes large and small delivery of five large boxes and six more boxes has a total weight of 175 kg a delivery of three large boxes and two small boxes has a total weight of 83 kg how much does each type of box weigh ?
large boxes --- x
small boxes --- y
5x+6y = 175
3x+2y = 83
multiply the 2nd by 3 and subtract it from 1st
5x + 6y = 175
9x + 6y = 249
4x = 74
x = 18.5
then in 3x+2y = 83
3(18.5) + 2y = 83
y = 13.75
state your conclusion
To find the weight of each type of box, we can set up a system of equations based on the given information.
Let's denote the weight of a large box as "L" and the weight of a small box as "S."
From the first statement, we know that 5 large boxes and 6 more boxes (which we will assume are small boxes) have a total weight of 175 kg. This can be expressed as the equation:
5L + 6S = 175 (Equation 1)
Similarly, from the second statement, we know that 3 large boxes and 2 small boxes have a total weight of 83 kg:
3L + 2S = 83 (Equation 2)
Now, we have two equations with two variables. We can solve this system of equations using various methods such as substitution, elimination, or matrices. Let's use the method of substitution:
1. Solve Equation 2 for L:
3L + 2S = 83
3L = 83 - 2S
L = (83 - 2S)/3
2. Substitute this value of L into Equation 1:
5L + 6S = 175
5((83 - 2S)/3) + 6S = 175
3. Simplify and solve for S:
(415 - 10S)/3 + 6S = 175
415 - 10S + 18S = 525
8S = 525 - 415
8S = 110
S = 110/8
S = 13.75
We have found the weight of a small box, which is 13.75 kg.
4. Substitute this value of S back into Equation 1 to find L:
5L + 6(13.75) = 175
5L + 82.5 = 175
5L = 175 - 82.5
5L = 92.5
L = 92.5/5
L = 18.5
Therefore, the weight of a large box is 18.5 kg.
In conclusion, each large box weighs 18.5 kg, and each small box weighs 13.75 kg.