John bought 8 apples and 10 oranges for a total of $41.60. An orange cost 70 cents less than an apple. What was the total cost of the apples?
a = apples cost
o = orange cost
70 cents = 0.7 $
An orange cost 70 cents less than an apple.
This mean :
o = a - 0.7 $
Total cost = 41.6 $
8 a * 10 o = 41.6
8 a + 10 ( a - 0.7 ) = 41.6
8 a + 10 a - 7 = 41.6
18 a - 7 = 41.6 Add 7 to both sides
18 a - 7 + 7 = 41.6 + 7
18 a = 48.6 Divide both sides by 18
18 a / 18 = 48.6 / 18
a = 2.7 $
o = a - 0.7 $
o = 2.7 $ - 0.7 $ = 2 $
Apple cost 2.7 $.
Orange cost 2 $.
Proff :
8 * a + 10 * o = 8 * 2.7 + 10 * 2 = 21.6 + 20 = 41.6 $
To find the total cost of the apples, let's first assign variables to represent the unknowns. Let's say the cost of each apple is A dollars and the cost of each orange is O dollars.
We know that John bought 8 apples and 10 oranges and the total cost was $41.60. This information can be expressed in the following equations:
8A + 10O = 41.60 (equation 1) - represents the total cost of the fruits
O = A - 0.70 (equation 2) - represents the cost of an orange being 70 cents less than an apple
Now, we can substitute equation 2 into equation 1 to solve for A.
8A + 10(A - 0.70) = 41.60
Simplifying the equation:
8A + 10A - 7 = 41.60
Combining like terms:
18A - 7 = 41.60
Adding 7 to both sides of the equation:
18A = 48.60
Dividing both sides by 18:
A = 2.70
So the cost of each apple is $2.70. To find the total cost of the apples, we multiply the cost of each apple by the number of apples John bought:
Total cost of apples = 8 * $2.70 = $21.60
Therefore, the total cost of the apples is $21.60.