Find x: Calculate Cucumber Price per kg Given $2.8/kg Tomatoes

Linear Equations with Mixed Unit Calculations

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 x x (in dollars).

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find X
00:03 Price per kg of tomatoes
00:09 We'll buy 2 kg of tomatoes
00:13 Amount of cucumbers in kg
00:16 Let's mark the price of cucumbers per kg using the unknown X
00:22 The total amount paid
00:29 Solve each multiplication separately
00:39 Let's arrange the equation so that one side has only the unknown X
00:53 Isolate X
00:58 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

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 x x (in dollars).

2

Step-by-step solution

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:
    2kg×2.8dollars/kg=5.6dollars 2 \, \text{kg} \times 2.8 \, \text{dollars/kg} = 5.6 \, \text{dollars} .

  • Step 2: Write the equation for total cost.
    The total cost for tomatoes and cucumbers combined is given as $7.1. Let x x represent the cost per kg of cucumbers. The equation representing the total cost is:
    5.6+0.6x=7.1 5.6 + 0.6x = 7.1 .

  • Step 3: Solve the equation for x x .
    Subtract the cost of tomatoes from both sides of the equation to find the cost of cucumbers:
    0.6x=7.15.6 0.6x = 7.1 - 5.6 .
    Simplifying the right side gives:
    0.6x=1.5 0.6x = 1.5 .

  • Step 4: Isolate x x by dividing both sides by 0.6:
    x=1.50.6 x = \frac{1.5}{0.6} .
    Simplify the division to find x x :
    x=2.5 x = 2.5 .

Therefore, the value per kg of cucumbers is x=2.5 x = 2.5 dollars.

3

Final Answer

x=2.5 x=2.5

Key Points to Remember

Essential concepts to master this topic
  • Setup: Calculate known costs first, then create equation for unknown
  • Technique: Cost of tomatoes: 2 kg × $2.8/kg = $5.6
  • Check: Verify: $5.6 + (0.6 × $2.5) = $5.6 + $1.5 = $7.1 ✓

Common Mistakes

Avoid these frequent errors
  • Using total quantities instead of unit prices
    Don't set up 2.8 + 0.6x = 7.1 using the unit price directly = wrong equation structure! This ignores the quantities purchased. Always multiply unit prices by their respective quantities first: (2 × 2.8) + (0.6 × x) = 7.1.

Practice Quiz

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\( \frac{-y}{5}=-25 \)

FAQ

Everything you need to know about this question

Why do I multiply the unit price by the quantity?

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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.

How do I know which variable represents what?

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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.

What if I get confused about which costs to add?

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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.

Can I solve this without setting up an equation?

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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.

How do I check if x = 2.5 is really correct?

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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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