To determine the number of goats Deepak has, we will solve the problem using a system of linear equations. Here’s the step-by-step solution:
1. Set up the variables:
Let [tex]\( h \)[/tex] represent the number of hens and [tex]\( g \)[/tex] represent the number of goats.
2. Establish the equations based on the problem statement:
- Each animal has one head, so the total number of heads (hens and goats) can be expressed as:
[tex]\[
h + g = 90
\][/tex]
- Hens have 2 feet each and goats have 4 feet each, so the total number of feet can be expressed as:
[tex]\[
2h + 4g = 248
\][/tex]
3. Solve the system of equations:
- From the first equation [tex]\( h + g = 90 \)[/tex], solve for [tex]\( h \)[/tex]:
[tex]\[
h = 90 - g
\][/tex]
- Substitute this expression for [tex]\( h \)[/tex] into the second equation:
[tex]\[
2(90 - g) + 4g = 248
\][/tex]
- Distribute the 2 in the equation:
[tex]\[
180 - 2g + 4g = 248
\][/tex]
- Combine like terms:
[tex]\[
180 + 2g = 248
\][/tex]
- Subtract 180 from both sides:
[tex]\[
2g = 68
\][/tex]
- Divide both sides by 2:
[tex]\[
g = 34
\][/tex]
4. Determine the number of hens:
- Substitute [tex]\( g = 34 \)[/tex] back into the equation [tex]\( h = 90 - g \)[/tex]:
[tex]\[
h = 90 - 34
\][/tex]
[tex]\[
h = 56
\][/tex]
Thus, Deepak has a total of [tex]\(\boxed{34}\)[/tex] goats.
