an algebra book weighs 6 oz less than twice as much as grammar book. if 5 algebra books weigh the same as 8 grammar books, how much does an algebra book weigh?
a = 2g-6
5a = 8g
5a = 8(a+6)/2
5a = 4a+12
a = 12
Let's first assign some variables to the unknown quantities in the problem.
Let's say the weight of the algebra book is A ounces.
According to the problem, the algebra book weighs 6 ounces less than twice the weight of the grammar book. Therefore, the weight of the grammar book can be represented as (A+6)/2 ounces.
Next, it is stated that 5 algebra books weigh the same as 8 grammar books. This can be expressed as:
5A = 8(A+6)/2
To solve this equation, let's first simplify the right side:
5A = 8(A+3)
Now, distribute the 8 to (A+3):
5A = 8A + 24
Subtract 8A from both sides to isolate the variable:
5A - 8A = 24
Simplifying further, we have:
-3A = 24
Now, divide both sides by -3:
A = -8
Since a weight cannot be negative, it seems there was an error in the problem statement or in the derivation of the equation. Please double-check the question or provide additional information so that I can assist you further.
To find out how much an algebra book weighs, we'll follow a step-by-step approach:
Let's assume that the weight of an algebra book is represented by 'A' and the weight of a grammar book is represented by 'G'.
Given:
1. The algebra book weighs 6 oz less than twice as much as the grammar book:
A = 2G - 6
2. Five algebra books weigh the same as eight grammar books:
5A = 8G
Now, we have two equations with two variables. We can solve this system of equations using substitution or elimination.
Using substitution method:
Step 1: Substitute the value of A from Equation 1 into Equation 2:
5(2G - 6) = 8G
Step 2: Simplify the equation:
10G - 30 = 8G
Step 3: Solve for G:
10G - 8G = 30
2G = 30
G = 15
Step 4: Substitute the value of G into Equation 1 to find A:
A = 2(15) - 6
A = 30 - 6
A = 24
Therefore, an algebra book weighs 24 ounces.