During its first week of business, a market sold a total of 108 apples and oranges. The second week, five times the number of apples and three times the number of oranges were sold. A total of 452 apples and oranges were sold during the second week. Determine how many apples and how many oranges were sold the first week.
a = apples
o = oranges
1 week :
a + o = 108
2 week :
5 a + 3 o = 452
Now you must solve system of 2 equations with 2 unknown :
a + o = 108
5 a + 3 o = 452
The method of substitution:
a + o = 108 Subtract o to both sides
a + o - o = 108 - o
a = 108 - o
5 a + 3 o = 452
5 * ( 108 - o ) + 3 o = 452
5 * 108 - 5 * o + 3 o = 452
540 - 5 o + 3 o = 452
540 - 2 o = 452 Subtract 540 to both sides
540 - 2 o - 540 = 452 - 540
- 2 o = - 88 Divide both sides by - 2
- 2 o / - 2 = - 88 / - 2
o = 44
a = 108 - o
a = 108 - 44 = 64
64 apples and 44 oranges
Why did the apple go to the therapist? Because it had some serious core issues!
Let's solve this fruitful problem, shall we? Let's assume the number of apples sold during the first week is 'A,' and the number of oranges sold is 'O.'
In the first week, the market sold a total of 108 apples and oranges, so we can write the equation: A + O = 108.
Now, during the second week, five times the number of apples, which is 5A, and three times the number of oranges, which is 3O, were sold. The total number of apples and oranges sold during the second week is 452, so we can write the equation: 5A + 3O = 452.
Now, let's solve this fruity situation using a little mathematical magic!
By multiplying the first equation by 3, we get 3A + 3O = 324.
Subtracting this new equation from the second equation, we get: (5A + 3O) - (3A + 3O) = 452 - 324.
Simplifying that equation, we have: 2A = 128.
And finally, dividing both sides of the equation by 2, we find that A, the number of apples sold the first week, is 64.
Substituting this value back into the first equation, we get: 64 + O = 108.
Solving for O, we find that O, the number of oranges sold the first week, is 44.
So, during the first week, the market sold 64 apples and 44 oranges.
Remember, life is like a box of apples and oranges - it's always full of surprises!
Let's assume the number of apples sold during the first week is 'A' and the number of oranges sold is 'O'.
According to the given information, during the first week, the market sold a total of 108 apples and oranges. Therefore, we can write the equation:
A + O = 108 ...........(1)
During the second week, five times the number of apples and three times the number of oranges were sold. So, we can write the equation:
5A + 3O = 452 ...........(2)
We now have a system of equations (1) and (2). We can solve this system of equations to find the values of A and O.
Let's solve the system of equations by substitution:
From equation (1), we can write:
A = 108 - O
Substituting this value of A in equation (2), we get:
5(108 - O) + 3O = 452
540 - 5O + 3O = 452
-2O = 452 - 540
-2O = -88
O = -88 / -2
O = 44
Now, we can substitute the value of O in equation (1) to find A:
A + 44 = 108
A = 108 - 44
A = 64
Therefore, during the first week, 64 apples and 44 oranges were sold.
Let's assume the number of apples sold during the first week is represented by 'a', and the number of oranges sold during the first week is represented by 'o'.
During the first week, a market sold a total of 108 apples and oranges, so we can write the equation:
a + o = 108
During the second week, five times the number of apples and three times the number of oranges were sold, so we can write another equation:
5a + 3o = 452
To solve this system of equations, we can use the method of substitution.
First, let's solve the first equation for 'a'. Subtracting 'o' from both sides, we get:
a = 108 - o
Now, substitute this expression for 'a' into the second equation:
5(108 - o) + 3o = 452
Expand and simplify:
540 - 5o + 3o = 452
Combine like terms:
-2o = 452 - 540
-2o = -88
Divide both sides by -2:
o = -88 / -2
o = 44
Now that we know the value of 'o' is 44, we can substitute it back into the first equation to solve for 'a':
a + 44 = 108
Subtract 44 from both sides:
a = 108 - 44
a = 64
Therefore, during the first week, 64 apples and 44 oranges were sold.