1 kg of tomatoes costs $2.8.
Maggie buys 2 kg of tomatoes and 0.6 kg of cucumbers, costing a total of $7.1.
Express the value per kg of cucumbers in terms of (in dollars).
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1 kg of tomatoes costs $2.8.
Maggie buys 2 kg of tomatoes and 0.6 kg of cucumbers, costing a total of $7.1.
Express the value per kg of cucumbers in terms of (in dollars).
To solve for the price per kg of cucumbers, follow these steps:
Step 1: Determine the total cost of tomatoes.
Given that the cost of tomatoes is $2.8 per kg, and Maggie buys 2 kg, the cost of tomatoes is calculated as:
.
Step 2: Write the equation for total cost.
The total cost for tomatoes and cucumbers combined is given as $7.1. Let represent the cost per kg of cucumbers. The equation representing the total cost is:
.
Step 3: Solve the equation for .
Subtract the cost of tomatoes from both sides of the equation to find the cost of cucumbers:
.
Simplifying the right side gives:
.
Step 4: Isolate by dividing both sides by 0.6:
.
Simplify the division to find :
.
Therefore, the value per kg of cucumbers is dollars.
\( \frac{-y}{5}=-25 \)
Unit prices tell you the cost per kilogram, but you need the total cost for your equation. If cucumbers cost $2.5/kg and you buy 0.6 kg, you pay 0.6 × $2.5 = $1.5 total.
The problem asks for x as the value per kg of cucumbers. This means x is the unit price (dollars per kilogram), not the total cost of cucumbers.
List what Maggie bought: 2 kg tomatoes + 0.6 kg cucumbers = $7.1 total. So your equation is: (cost of 2 kg tomatoes) + (cost of 0.6 kg cucumbers) = $7.1.
You could subtract the tomato cost from the total, then divide by 0.6, but setting up the equation 0.6x + 5.6 = 7.1 helps you organize your thinking and avoid calculation errors.
Substitute back: Total cost = (2 kg × $2.8/kg) + (0.6 kg × $2.5/kg) = $5.6 + $1.5 = $7.1 ✓. This matches the given total!
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