1. Let t be the number of toppings.
Equation for Palanzio’s: C_p = 6.80 + 0.90t
Equation for Guido’s: C_g = 7.30 + 0.65t
Set equal: 6.80 + 0.90t = 7.30 + 0.65t
Solve: 0.25t = 0.50 → t = 2
Answer: 2 toppings.
2. Let l = CDs sold last week, t = CDs sold this week.
Equation 1: l = 3t + 6
Equation 2: l + t = 110
Substitute: (3t + 6) + t = 110 → 4t + 6 = 110 → 4t = 104 → t = 26
Then l = 3(26) + 6 = 84
Answer: l = 84, t = 26.
3. Let w = width, l = length.
Equation 1: l = 3w
Equation 2: 2l + 2w = 86
Substitute: 2(3w) + 2w = 86 → 6w + 2w = 86 → 8w = 86 → w = 10.75
Then l = 3(10.75) = 32.25
Answer: width = 10.75 cm, length = 32.25 cm.
4. Let t = cost of a taco, m = cost of a small glass of milk.
Equation 1: t + m = 2.10
Equation 2: 2t + 3m = 5.15
Multiply Eq1 by 2: 2t + 2m = 4.20
Subtract from Eq2: (2t + 3m) - (2t + 2m) = 5.15 - 4.20 → m = 0.95
Then t = 2.10 - 0.95 = 1.15
Answer: t = $1.15, m = $0.95.
Parent Tip: Review the logic above to help your child master the concept of systems of equations 3 variables word problems worksheet.
