Question

Will bought 8 bagels and 5 muffins that cost him $28.85.Gale went to the same store and bought 6 bagels and 7 muffins costing $26.09. Abby went to the same store and bought 2 bagels and some muffins and spent $9.61. How many muffins did she buy?

Answer 1

Answer:

$\boxed{3}$

Step-by-step explanation:

1. Set up the equations

 Let b = the cost of a bagel

and m = the cost of a muffin

You have a system of two equations:

$\begin{cases}(1) & 8b + 5m = 28.85\\(2) & 6b + 7m = 26.09\end{cases}$

2. Solve the equations

$\begin{array}{lrcll}(3) & 56b + 35m & = & 201.95 &\text{Multiplied (1) by 7}\\(4) & 30b + 35m & = & 130.45 &\text{Multiplied (2) by 5}\\ & 26b & = & 71.50 &\text{Subtracted (4) from (3)}\\(5) & b & = & 2.75 &\text{Divided each side by 26} \\& 6\times 2.75 + 7m & = & 26.09 & \text{Substituted (5) into (2)}\\& 16.50 + 7m& = & 26.09 & \text{Simplified}\\& 7m & = & 9.59 & \text{Subtracted 16.50 from each side}\\& m& = & 1.37 & \text{Divided each side by 7}\\\end{array}$

3. Calculate the number of muffins Abby bought

Let x = the number of muffins. Then

$\begin{array}{rcl}2b + mx & = & 9.61\\2 \times 2.75 + 1.37x & = & 9.61\\5.50 + 1.37x & = & 9.61\\1.37x & = & 4.11\\x & = & \mathbf{3}\\\end{array}\\\text{Abby bought \boxed{\mathbf{3}} muffins}$