Question

Jacob has to buy treats for his class. He can buy 105 tootsie rolls and 35 sweetarts for $7.35 or he can buy 35 tootsie rolls and 70 sweetarts for $11.20. How much do individual tootsie rolls and sweetarts cost?​

Answer 1

Each individual tootsie roll costs $0.05 and each individual sweetheart costs $0.135.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's represent the cost of an individual tootsie roll as x and the cost of an individual sweetheart as y. From the given information, we can create two equations:

105x + 35y = 7.35 (Equation 1)

35x + 70y = 11.20 (Equation 2)

To solve this system, we can use the method of substitution or elimination. Let's use the method of elimination:

Multiplying Equation 1 by 2 and Equation 2 by -3, we get:

210x + 70y = 14.70 (Equation 3)

-105x - 210y = -33.60 (Equation 4)

Adding Equation 3 and Equation 4, we eliminate the x variable:

-140y = -18.90

Dividing both sides by -140, we find that y = 0.135

Substituting this value of y back into Equation 1 or Equation 2, we can solve for x:

35x + 70(0.135) = 11.20

35x + 9.45 = 11.20

35x = 1.75

x = 0.05

Therefore, each individual tootsie roll costs $0.05 and each individual sweetheart costs $0.135.