The walnut cove ruritan club sells hot dogs and drinks from a concession stand at the annual july 4 parade. carl bought 6 hot dogs and 4 drinks, paying $17.00. susan purchased 3 hot dogs and 4 drinks and was charged $12.50. what's the cost of 1 hot dog, and what's the cost of 1 drink? a. $2.50 for a hot dog; $1.00 for a drink b. $1.40 for a hot dog; $2.15 for a drink c. $1.60 for a hot dog; $1.85 for a drink d. $1.50 for a hot dog; $2.00 for a drink

Based on the two different purchases, you can write equations for the price of a hotdog (h) and that of a drink (d). These equations can be solved by your favorite method to find the individual prices.

... 6h +4d = 17.00 . . . . . . Carl's purchase

... 3h +4d = 12.50 . . . . . . Susan's purchase

We can see that the difference in purchase cost (of $4.50) is due entirely to the difference in the number of hotdogs (3). Thus, the price of a hotdog must be

... $4.50/3 = $1.50

The 4 drinks are then ($12.50 -4.50) = $8, so must be $2 each. You don't need to figure the cost of a drink to determine that the appropriate answer choice is ...

... D. $1.50 for a hot dog; $2.00 for a drink.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.