The cost of making a dress is partly constant and partly varies with the amount of time it takes to make the dress.if the dress takes 3 hours to make the dress,it cost 3100 naira.find the cost if it takes 1.5 hours to make the dress.

Question

The cost of making a dress is partly constant and partly varies with the amount of time it takes to make the dress.if the dress takes 3 hours to make the dress,it cost 3100 naira.find the cost if it takes 1.5 hours to make the dress.

Answer 1

To find the cost if it takes 1.5 hours to make the dress, we can use the concept of variation.

Let's denote the constant cost as C and the variable cost per hour as V. We know that when it takes 3 hours to make the dress, the cost is 3100 naira.

So we can set up the equation:
C + V*3 = 3100

Now, we can solve for C by substituting the values and simplifying the equation:

C + V*3 = 3100
C + 3V = 3100

Similarly, when it takes 1.5 hours to make the dress, we can set up the equation:
C + V*1.5 = ?

Since we want to find the cost, we'll use a question mark "?" to represent the unknown value.

Now, we can substitute the values of C and V from the previous equation into this new equation:
(C + 3V)/2 = ?

Substituting the known values from the previous equation:
(3100 + 3V)/2 = ?

Multiplying both sides by 2 to eliminate the denominator:
3100 + 3V = ? * 2
3100 + 3V = 2?

Now we have two equations:
C + 3V = 3100
3100 + 3V = 2?

We can solve these equations to find the values of C and V.

Answer 2

To solve this problem, we need to first find the constant cost of making the dress and the cost that varies with the amount of time.

Let's assume the constant cost is C and the cost that varies with time is T.

From the given information, we know that if it takes 3 hours to make the dress, the cost is 3100 Naira.

Thus, we have the equation:
3T + C = 3100

Now, we can find the value of C by substituting the given information:
3T + C = 3100
3(3) + C = 3100
9 + C = 3100
C = 3100 - 9
C = 3091

Now, we can find the cost if it takes 1.5 hours to make the dress.

Substituting the values into the equation, we get:
1.5T + 3091 = Cost

However, we don't know the value of T.

To find T, we can use the information from the previous equation:
3T + C = 3100
3T + 3091 = 3100
3T = 3100 - 3091
3T = 9
T = 3

Substituting T = 3 into the equation for the cost with 1.5 hours, we get:
1.5(3) + 3091 = Cost
4.5 + 3091 = Cost
3095.5 = Cost

Therefore, if it takes 1.5 hours to make the dress, the cost would be 3095.5 Naira.