Word Problem: Show steps and answer each question in a complete sentence.
1) Ada made 137 baked goods and charged $5 for a brownie and $2 for a cookie. She sold them and made $400 in all. How many brownies and how many cookies did she make?
Let's assume Ada made x brownies and y cookies.
- From the problem, we know that Ada made a total of 137 baked goods, so we can write the equation: x + y = 137.
- We also know that Ada charged $5 for each brownie, so the total earnings from the brownies would be 5x.
- Similarly, Ada charged $2 for each cookie, so the total earnings from the cookies would be 2y.
- The problem states that Ada made a total of $400, so we can write the equation: 5x + 2y = 400.
Using these equations, we can now solve for x and y.
From the first equation, we can solve for y in terms of x: y = 137 - x.
Substituting this value of y into the second equation, we have:
5x + 2(137 - x) = 400
5x + 274 - 2x = 400
3x = 400 - 274
3x = 126
x = 126 / 3
x = 42
Substituting the value of x back into the first equation, we have:
42 + y = 137
y = 137 - 42
y = 95
Therefore, Ada made 42 brownies and 95 cookies.