Fearing the chance of a 3rd covid wave akansha went to the local medical store to buy some masks sanitizer and gloves she saw that the cost of buying 2 masks 7 gloves and 12 sanitizers is 350 and cost of buying 1 mask 3 gloves and 5 sanitizer is 155 then how much money did she spend if she bought 1 mask 1 glove and 1 sanitizer?

Let's denote the cost of one mask as \( m \), one glove as \( g \), and one sanitizer as \( s \).

Given the information:

1. The cost of buying 2 masks, 7 gloves, and 12 sanitizers is 350:
   \[
   2m + 7g + 12s = 350
   \]

2. The cost of buying 1 mask, 3 gloves, and 5 sanitizers is 155:
   \[
   m + 3g + 5s = 155
   \]

We need to find the cost of buying 1 mask, 1 glove, and 1 sanitizer, i.e., we need to find the value of \( m + g + s \).

### Step 1: Solve the system of equations

We have the system:
\[
\begin{aligned}
2m + 7g + 12s &= 350 \quad \text{(1)} \\
m + 3g + 5s &= 155 \quad \text{(2)}
\end{aligned}
\]

### Step 2: Eliminate one variable

To eliminate \( m \), multiply equation (2) by 2:
\[
2m + 6g + 10s = 310 \quad \text{(3)}
\]

Now, subtract equation (3) from equation (1):
\[
(2m + 7g + 12s) - (2m + 6g + 10s) = 350 - 310
\]
\[
g + 2s = 40 \quad \text{(4)}
\]

### Step 3: Substitute back to find \( m \)

Now substitute \( g = 40 - 2s \) from equation (4) into equation (2):
\[
m + 3(40 - 2s) + 5s = 155
\]
\[
m + 120 - 6s + 5s = 155
\]
\[
m - s = 35 \quad \text{(5)}
\]

### Step 4: Express \( m + g + s \)

From equation (5):
\[
m = s + 35
\]
Now substitute \( m = s + 35 \) and \( g = 40 - 2s \) into \( m + g + s \):
\[
m + g + s = (s + 35) + (40 - 2s) + s
\]
\[
m + g + s = 75
\]

### Conclusion:
Akansha spent **75** units of money to buy 1 mask, 1 glove, and 1 sanitizer.

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Would you like more details or have any questions about this solution? 

Here are some related questions for further exploration:

1. What would be the cost if Akansha bought 2 masks, 2 gloves, and 2 sanitizers?
2. How much would 3 masks, 4 gloves, and 6 sanitizers cost?
3. If the cost of the mask increased by 10 units, how would that affect the total cost?
4. What would be the cost of 5 gloves and 10 sanitizers?
5. How much would Akansha spend if she bought twice the quantity of everything?
6. What if the price of sanitizer was reduced by half? How would the total cost change?
7. Can you derive the cost of 1 mask, 1 glove, and 1 sanitizer using another method?
8. What would be the total cost if Akansha bought 3 masks, 3 gloves, and 3 sanitizers?

**Tip:** When solving a system of linear equations, eliminating one variable by substitution or elimination can simplify the process significantly.

Find out how much money Akansha spent on masks, gloves, and sanitizers based on given pricing details and purchase quantities. Detailed step-by-step solution included.

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