What is the cost of 1 cup of coffee?

Question image

Understand the Problem

The question is asking to solve a system of equations to determine the cost of one cup of coffee. The equations provided relate the costs of coffee and doughnuts purchased by two customers.

Answer

The cost of 1 cup of coffee is $2.50.
Answer for screen readers

The cost of 1 cup of coffee is $c = 2.50$.

Steps to Solve

  1. Identify the system of equations

The given equations are: $$ c + 2d = 4.90 \quad (1) $$ $$ 2c + 3d = 8.60 \quad (2) $$

  1. Solve equation (1) for one variable

From equation (1), isolate $c$: $$ c = 4.90 - 2d $$

  1. Substitute into equation (2)

Replace $c$ in equation (2) with the expression found from equation (1): $$ 2(4.90 - 2d) + 3d = 8.60 $$

  1. Simplify the equation

Distribute and combine like terms: $$ 9.80 - 4d + 3d = 8.60 $$ $$ 9.80 - d = 8.60 $$

  1. Solve for $d$

Rearrange the equation to solve for $d$: $$ -d = 8.60 - 9.80 $$ $$ -d = -1.20 $$ $$ d = 1.20 $$

  1. Substitute $d$ back into equation (1)

Using the value of $d$ in equation (1) to find $c$: $$ c + 2(1.20) = 4.90 $$ $$ c + 2.40 = 4.90 $$

  1. Solve for $c$

Rearranging gives: $$ c = 4.90 - 2.40 $$ $$ c = 2.50 $$

The cost of 1 cup of coffee is $c = 2.50$.

More Information

The problem uses a system of linear equations to find the cost of coffee and doughnuts. It's a common method in algebra to determine unknowns based on known relationships.

Tips

  • Failing to rearrange equations correctly when isolating variables.
  • Miscalculating when substituting values back into equations.
  • Forgetting to reduce or simplify terms properly during calculations.
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