3. In a fruit bowl there are twice as many apples as oranges.
Altogether there are 12 pieces of fruit.
Explain what the information is shown in the following equation. A + O =12.
Explain what information is shown in the following equation. A= O+O
How many of each fruit are there?
A + O =12: Altogether there are 12 pieces of fruit.
A = O+O: twice as many apples as oranges
8+4 = 12
How many pieces of fruits are in bowl altogether
The equation A + O = 12 represents the total number of pieces of fruit in the fruit bowl, which is 12.
The equation A = O + O represents the relationship between the number of apples (A) and the number of oranges (O), stating that the number of apples is equal to two times the number of oranges.
To find out how many of each fruit there are, we need to solve the system of equations. Since we know that A = O + O, we can substitute this into the first equation:
(O + O) + O = 12
Simplifying,
3O = 12
Dividing both sides by 3,
O = 4
So, there are 4 oranges in the fruit bowl.
To find the number of apples, we can substitute the value of O back into A = O + O:
A = 4 + 4 = 8
Therefore, there are 8 apples in the fruit bowl.
The equation A + O = 12 represents the total number of pieces of fruit in the bowl. The variables A and O represent the number of apples and oranges, respectively. By adding the numbers together, we get a sum of 12, which represents the total count of fruit in the bowl.
The equation A = O + O shows that the number of apples (A) is equal to twice the number of oranges (O). This equation reflects the information given in the problem that there are twice as many apples as oranges in the fruit bowl.
To find out how many of each fruit there are, we can use substitution or the method of solving simultaneous equations.
Substitution method:
Since we know that A = O + O, we can substitute this value into the equation A + O = 12 to get (O + O) + O = 12. Simplifying, we get 3O = 12, which means O = 4.
Now we can substitute the value of O back into the equation A = O + O: A = 4 + 4, which gives us A = 8.
Therefore, there are 8 apples and 4 oranges in the fruit bowl.