To find the number of cups of sugar needed for Recipe A, we can set up an equation using the given information. Recipe A calls for one-third less than twice the number of cups of sugar in Recipe B. Solving the equation, we find that Recipe A will need 3 and 3/8 cups of sugar.
To find the number of cups of sugar needed for Recipe A, we can set up an equation using the given information. Let's assume that Recipe B calls for x cups of sugar. According to the problem, Recipe A calls for one-third less than twice the number of cups of sugar in Recipe B. So, Recipe A would need a total of 2x - (1/3)(2x) cups of sugar. We are also given that the total amount of sugar needed for both recipes is four and one-sixths cups. Therefore, we can write the equation:
2x - (1/3)(2x) = 4 + 1/6
To solve this equation, we can simplify the expression on the left-hand side:
2x - (2/3)x = 4 + 1/6
Combining like terms, we get:
(6/3)x - (2/3)x = 4 + 1/6
Simplifying further, we have:
(4/3)x = 4 + 1/6
To isolate x, we can multiply both sides of the equation by the reciprocal of 4/3, which is 3/4:
(3/4)(4/3)x = (3/4)(4 + 1/6)
Canceling out the common factors, we get:
x = (3/4)(4 + 1/6)
Evaluating the right-hand side of the equation:
x = (3/4)(25/6)
Multiplying the fractions, we have:
x = (75/24)
Simplifying the fraction, we get:
x = 3 + 3/8
Therefore, Recipe A will need 3 and 3/8 cups of sugar.
the complete Question is given below:
Morgan is making two cookie recipes. Recipe A calls for one-third less than twice the number of cups of sugar that Recipe B calls for. If she needs four and one-sixths cups of sugar in all, how many cups will she need for Recipe A?