Sure, let's solve this problem step-by-step.
Let's denote the number of baskets Meena makes per hour as [tex]\( M \)[/tex] and the number of baskets Rena makes per hour as [tex]\( R \)[/tex].
We are given two pieces of information:
1. In three hours, Meena makes one basket more than what Rena makes in two hours.
2. In five hours, Meena makes one basket less than what Rena makes in four hours.
We can translate these statements into mathematical equations.
### Step 1: Translate the first piece of information
"In three hours, Meena makes one basket more than what Rena makes in two hours."
[tex]\[ 3M = 2R + 1 \][/tex]
### Step 2: Translate the second piece of information
"In five hours, Meena makes one basket less than what Rena makes in four hours."
[tex]\[ 5M = 4R - 1 \][/tex]
### Step 3: Solving the system of equations
We now have the following system of linear equations:
1. [tex]\( 3M = 2R + 1 \)[/tex]
2. [tex]\( 5M = 4R - 1 \)[/tex]
Let's solve these equations simultaneously.
First, solve the first equation for [tex]\( R \)[/tex]:
[tex]\[ 3M = 2R + 1 \][/tex]
[tex]\[ 2R = 3M - 1 \][/tex]
[tex]\[ R = \frac{3M - 1}{2} \quad (1) \][/tex]
Next, substitute this expression for [tex]\( R \)[/tex] into the second equation:
[tex]\[ 5M = 4R - 1 \][/tex]
[tex]\[ 5M = 4 \left( \frac{3M - 1}{2} \right) - 1 \][/tex]
[tex]\[ 5M = 2(3M - 1) - 1 \][/tex]
[tex]\[ 5M = 6M - 2 - 1 \][/tex]
[tex]\[ 5M = 6M - 3 \][/tex]
[tex]\[ 5M - 6M = -3 \][/tex]
[tex]\[ -M = -3 \][/tex]
[tex]\[ M = 3 \][/tex]
So, Meena can make 3 baskets per hour.
Therefore, the number of baskets Meena can make in an hour is [tex]\(\boxed{3}\)[/tex].
