Ronnie went to the bookstore and bought some books. He paid 1/6 of the total cost with cash, 2/4 with a check, and the remaining 0.4 multiplied by 5 with a credit card. In total, he spent $20. How much did the books cost?
AAAaannndd the bot gets it wrong yet again!
Let's denote the total cost of the books as "C" in dollars.
According to the given information, Ronnie paid 1/6 of the total cost with cash, which is (1/6)C dollars.
He also paid 2/4 of the total cost with a check, which is (2/4)C dollars.
The remaining amount, which is paid with a credit card, is 0.4 multiplied by 5 times the total cost, which is 0.4(5C) dollars.
The total amount Ronnie spent is given as $20.
So, we can set up the equation:
(1/6)C + (2/4)C + 0.4(5C) = 20
To simplify the equation, we can convert the fractions into decimals:
(1/6)C + (1/2)C + 0.4(5C) = 20
Now, let's solve the equation step by step:
1/6C + 1/2C + 0.4(5C) = 20
Multiplying 0.4 by 5C:
1/6C + 1/2C + 2C = 20
Adding the fractions:
(1/6 + 1/2)C + 2C = 20
Finding a common denominator:
(1/6 + 3/6)C + 2C = 20
Combining the fractions:
4/6C + 2C = 20
Simplifying the left side:
(4/6 + 12/6)C = 20
Combining the fractions:
16/6C = 20
Dividing both sides by 16/6:
C = 20 / (16/6)
Dividing 20 by 16/6:
C = 20 * (6/16)
Simplifying the right side:
C = 120 / 16
C = 7.5
Therefore, the cost of the books is $7.5.
To find out how much the books cost, we can start by breaking down the information given.
Let's assign a variable to represent the total cost of the books. We'll use "x" for this.
According to the information given:
- Ronnie paid 1/6 of the total cost with cash, which is (1/6)x dollars.
- Ronnie paid 2/4 of the total cost with a check, which is (2/4)x dollars.
- Ronnie paid 0.4 multiplied by 5 of the remaining cost with a credit card, which is (0.4 * 5)(x - [(1/6)x + (2/4)x]). Simplifying this gives us 2(x - [(1/6)x + (2/4)x]).
Now let's add up the amounts Ronnie paid with each method:
(1/6)x + (2/4)x + 2(x - [(1/6)x + (2/4)x]) = 20
To solve for x, we can simplify the equation and solve it step by step:
(1/6)x + (2/4)x + 2(x - [(1/6)x + (2/4)x]) = 20
Multiply the terms inside the brackets by the number in front of the brackets:
(1/6)x + (2/4)x + 2(x - [x/6 + x/2]) = 20
Simplify the fractions inside the brackets:
(1/6)x + (2/4)x + 2(x - (1/6)x - (1/2)x) = 20
Combine like terms inside the brackets:
(1/6)x + (2/4)x + 2(x - (2/3)x) = 20
Simplify further:
(1/6)x + (2/4)x + 2(x - (2/3)x) = 20
(1/6)x + (1/2)x + 2(x - (2/3)x) = 20
Now we can simplify the equation and solve for x:
Multiply out the fractions:
(1/6)x + (1/2)x + 2(x - (2/3)x) = 20
(x/6) + (x/2) + 2(x - (2/3)x) = 20
Common denominator for (x/6) and (x/2) is 6:
(x/6) + (3x/6) + 2(x - (2/3)x) = 20
Simplify:
(4x/6) + 2(x - (2/3)x) = 20
(2x/3) + 2(x - (2/3)x) = 20
Multiply out the terms inside the parentheses:
(2x/3) + 2(x - 2x/3) = 20
(2x/3) + 2(x - 2x/3) = 20
Simplify the terms inside the parentheses:
(2x/3) + 2(x - 2x/3) = 20
Multiply out the terms inside the parentheses:
(2x/3) + 2(3x/3 - 2x/3) = 20
(2x/3) + 2(3x - 2x)/3 = 20
Simplify further:
(2x/3) + 2x/3 = 20
Combine like terms:
4x/3 = 20
Multiply both sides by 3 to isolate x:
4x = 60
Divide both sides by 4:
x = 15
So the total cost of the books is $15.