Question

Solve the following
Trudy bought 3 hot dogs and 1 bag of fries for $315.if she had bought 2 hot dogs and 2 bags of fries it wold have cost $270

i. what is the cost of a hot dog

ii. what is the cost of a bag of fries

Answer 1

★ Given:-

• Cost of 3 hot dogs and 1 bag of fries = $315

• Cost of 2 hot dogs and 2 bag of fries = $270

★ To Find:-

• Cost of a hot dog

• Cost of a bag of fries

★ Solution:-

⟴ Let the cost of a hot dog be x

⟴ Let the cost of a bag of fries be y

Hence,

▪︎Cost of 3 hot dog be 3x

▪︎Cost of 1 bag of fries be y

▪︎Cost of 2 hot dogs be 2x

▪︎Cost of 2 bag of fries be 2y

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⟴ According to given conditions;

3x + y = $315 -------------- eq. ①

2x + 2y = $270 ----------- eq. ②

⟴ Multiplying 2 in eq. ①

2 ( 3x + y) = 2 × 315

➟ 6x + 2y = $630 -------- eq. ③

⟴ Multiplying 3 in eq. ②

3 ( 2x + 2y ) = 3 × 270

➟ 6x + 6y = $810 --------- eq. ④

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⟴ Subtracting eq. ③ from eq. ④

6x + 6y - ( 6x + 2y ) = 810 - 630

➟ 6x + 6y - 6x - 2y = 180

➟ 6x - 6x + 6x - 2y = 180

➟ 0 + 4y = 180

➟ y = 180 ÷ 4

➟ y = 45

∴ y = Cost of a bag of fries = $45

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⟴ According to given conditions;

3x + y = $315

⟴ Putting value of y in equation

➟ 3x + 45 = 315

➟ 3x = 315 - 45

➟ 3x = 270

➟ x = 270 ÷ 3

➟ x = 90

∴ x = cost of a hot dog = $90

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★ Answer:-

• Cost of a hot dog is $90.

• Cost of a bag of fries is $45.