Material cost of a fan belt is three-elevenths of total cost, and labour cost is five-ninths of material cost. If labour cost is $15, what is total cost of the fan belt?
Let's assume the total cost of the fan belt is x dollars.
The material cost is three-elevenths of the total cost, which means it is (3/11) * x dollars.
The labour cost is five-ninths of the material cost, which means it is (5/9) * (3/11) * x dollars.
Given that the labour cost is $15, we can set up the equation:
(5/9) * (3/11) * x = $15
Multiplying the fractions:
(15/99) * x = $15
To isolate x, we can multiply both sides of the equation by 99/15:
x = $15 * (99/15)
Simplifying:
x = $99
Therefore, the total cost of the fan belt is $99. Answer: \boxed{99}.
Let's start by finding the cost of materials. We know that the material cost is three-elevenths of the total cost. Since we don't know the total cost, let's represent it as "x". Therefore, the material cost would be (3/11) * x.
Next, we can find the labor cost, which is stated to be five-ninths of the material cost. So, the labor cost would be (5/9) * (3/11) * x.
We are given that the labor cost is $15. So we can set up the equation:
(5/9) * (3/11) * x = $15
Now, let's solve for x, the total cost of the fan belt.
(5/9) * (3/11) * x = $15
To simplify the equation, we can find the product of the fractions:
(15/99) * x = $15
Next, let's isolate x by multiplying both sides of the equation by the reciprocal of (15/99), which is (99/15):
(15/99) * x * (99/15) = $15 * (99/15)
Simplifying further:
x = $15 * (99/15)
x = $99
Therefore, the total cost of the fan belt is $99.
To find the total cost of the fan belt, we need to work step by step.
Step 1: Find the material cost.
Given that the material cost is three-elevenths of the total cost, we can represent it as:
Material Cost = (3/11) * Total Cost
Step 2: Find the labor cost.
Given that the labor cost is five-ninths of the material cost and is equal to $15, we can represent it as:
Labor Cost = (5/9) * Material Cost
Step 3: Find the material cost using the labor cost.
To find the material cost, let's rearrange the labor cost equation:
Material Cost = Labor Cost / (5/9)
Substituting the given labor cost ($15) into the equation, we have:
Material Cost = $15 / (5/9) = $27
Step 4: Find the total cost.
Now that we have the material cost, we can calculate the total cost by substituting it into the material cost equation:
Total Cost = (11/3) * Material Cost
Substituting the calculated material cost ($27) into the equation, we get:
Total Cost = (11/3) * $27 = $99
Therefore, the total cost of the fan belt is $99.