Problema Solution
Rachel can buy licorice sticks for $0.75 and cherry candies for $0.50 and has a budget of $25. If her expenses are represented by the equation 0.75x + 0.5y = 25, where x is the number of licorice sticks and y is the number of cherry candies, how many cherry candies can she buy if she wishes to spend the entire $25 on cherry candies? (Note: x ≥ 0, y ≥ 0, and x and y take only integer values.
Answer provided by our tutors
0.75x + 0.5y = 25
by solving for y we get:
y = 50 - (3/2)x
click here to see the step by step solution:
since y is an integer and y > 0 we have:
x is an even number and
50 - (3/2)x >= 0
that is:
x <= 33.3
click here to see the step by step solution of the inequality:
thus x can be an element of the set {0, 2, 4, 6, 8, ..., 32}
in that case the possible values for y are the elements of the set {2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50}
she can buy one of the following numbers of cherry candies: 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47 or 50.