How can algebra be used to solve this problem?

The boy solved 10 problems correctly at 8 cents a problem for a total of 80 cents, and 16 incorrectly at the cost of 5 cents for a total of 80 cents. Therefore, neither the boy nor his father owed each other anything at the end of the 26 problems.

What problem are we solving?

Everything appears to be explicitly stated.

Do you want us to figure out what the original problem was ?

It could have been something like this:
A father gave 26 math problems for his son to solve and said, "I will give you 8 cents for each problem you solve correctly, but you will lose 5 cents for problem you solve incorrectly".
If, at the end they broke even, how many problems did the son get right and how many did he get wrong?

the equation for that would be
8x = 5(26-x)

Thanks!

To understand how algebra can be used to solve this problem, let's break it down step by step:

1. First, let's define the variables:
- Let x be the number of problems solved correctly at 8 cents per problem.
- Let y be the number of problems solved incorrectly at 5 cents per problem.

2. Now we can set up the equations based on the given information:
- The boy solved 10 problems correctly at 8 cents per problem, so we have the equation: 8x = 80.
- The boy solved 16 problems incorrectly at 5 cents per problem, so we have the equation: 5y = 80.

3. Simplifying the equations:
- The first equation simplifies to x = 10.
- The second equation simplifies to y = 16.

4. Next, let's check if the boy and his father owe each other any money. The total cost for the correctly solved problems should be equal to the total cost for the incorrectly solved problems:
- The total cost for the correctly solved problems is 8 * 10 = 80 cents.
- The total cost for the incorrectly solved problems is 5 * 16 = 80 cents.

5. Since the total cost for both types of problems is the same, neither the boy nor his father owe each other anything at the end of the 26 problems.

In this problem, algebra helped us define variables, set up equations, and solve for those variables. The equations allowed us to find the number of correctly and incorrectly solved problems, and ultimately determine that no money was owed at the end.