SOLUTION
Given the question, the following are the solution steps to answer the question.
STEP 1: Write the given information

STEP 2: Represent the type of clients
Let a be the type of A client
Let b be the type of B client
Let c be the type of C client
STEP 3: Get the needed equations
Based on the information given, we can see that:
For the total clients, we have:

For the counselling:

For emergency foods:

STEP 4: Solve the equations simultaneously

Substitute into equation 2 and 3:

By Simplification we have:

Make y the subject of equation 4

Substitute the value into equation 5
![\begin{gathered} [-200((-c+600)/(3))-400c+360000]=220000 \\ By\text{ simplification,} \\ [(200c-120000)/(3)-400c]=220000-360000 \\ Multiply\text{ through by 3} \\ 200c-120000-1200c=-4200000 \\ -1000c=-420000+120000=-300000 \\ c=(-300000)/(-1000)=300 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/b28xswnwkby5iqx5dnq0vw1t7w3z8hzygi.png)
c = 300
STEP 5: Solve for b

b = 100
STEP 6: Solve for a
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Hence,
200 type A clients can be served
100 type B clients can be served
300 type C clients can be served