Question

Ain’t Your Mama’s Syrup is 50% pure maple syrup. Mrs. Butter Better’s syrup is 60% maple syrup. How much of each is needed to make a 100 ounce solution that is 51% maple syrup?

Answer 1

To create a 51% maple syrup 100-ounce solution, 90 ounces of Ain’t Your Mama’s Syrup (50% maple syrup) and 10 ounces of Mrs. Butter Better’s syrup (60% maple syrup) are needed.

Step-by-step explanation:

To find out how much of each syrup is needed to make a 100-ounce solution that is 51% maple syrup, we can set up a system of equations to represent the situation. Let x be the amount of Ain’t Your Mama’s Syrup (50% pure maple syrup) and y be the amount of Mrs. Butter Better’s syrup (60% maple syrup). The total amount of the mixture should be 100 ounces, and the overall concentration should be 51%. The equations would be:

• x + y = 100 (The total solution must be 100 ounces)
• 0.50x + 0.60y = 51 (51% of the total 100 ounces)

By solving these equations, we can find the values of x and y:

1. Multiply the first equation by -0.50 to prepare for elimination: -0.50x -0.50y = -50
2. Add this new equation to the second one: -0.50x -0.50y = -50 + 0.50x + 0.60y = 51
3. Simplify and solve for y: 0.10y = 1, so y = 10 ounces
4. Substitute the value of y back into x + y = 100 to find x: x + 10 = 100, so x = 90 ounces

Therefore, to create a 100-ounce solution that is 51% maple syrup, we need 90 ounces of Ain’t Your Mama’s Syrup and 10 ounces of Mrs. Butter Better’s syrup.