At a coffee house, each Americano costs $4, and each Latte costs d more dollars than an Americano. If three Americanos and four Lattes cost a total of $30, what is the value of d?

Let's start by setting up the equations based on the information given.

1. The cost of one Americano is $4.
2. The cost of one Latte is $ 4 + d $ dollars.

Now, we're told that the cost of three Americanos and four Lattes is $30. We can express this as an equation:

\[
3 \times 4 + 4 \times (4 + d) = 30
\]

Simplify the equation step by step:

\[
12 + 4 \times (4 + d) = 30
\]

Distribute the 4 across the terms inside the parentheses:

\[
12 + 16 + 4d = 30
\]

Combine the constant terms:

\[
28 + 4d = 30
\]

Now, isolate $ d $ by subtracting 28 from both sides:

\[
4d = 2
\]

Finally, solve for $ d $ by dividing both sides by 4:

\[
d = \frac{2}{4} = 0.5
\]

So, the value of $ d $ is **0.5**.

Would you like any further details on this problem, or have any other questions?

Here are five related questions for further practice:

1. If the price of each Latte were $ 4 + 2d $ dollars, what would the value of $ d $ be given the same total cost?
2. How would the value of $ d $ change if the total cost for three Americanos and four Lattes was $35 instead of $30?
3. What would be the cost of five Americanos and six Lattes with the original value of $ d $?
4. How many Americanos could you buy with $30 if $ d = 0.75 $?
5. What is the percentage increase in the cost from an Americano to a Latte if $ d = 0.5 $?

**Tip:** When solving word problems, clearly define variables and write equations that reflect the relationships described. This will help you solve the problem systematically.

Learn how to solve the coffee house math problem where Americanos cost $4 each, and Lattes cost $4 plus d dollars. Calculate the value of d given the total cost of three Americanos and four Lattes is $30. Detailed step-by-step solution provided.

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