Question

practice problems

1. a car travels 55 miles per hour (mph) for 2 hr. complete the table.

time (hr.)	distance (mi.)	speed (mph)
\\(\frac{1}{2}\\)	29.5	55
\\(1\frac{1}{2}\\)	82.5	55
2	110	55

1. the table shows the ounces (oz.) of onions and tomatoes in different-sized batches of a salsa recipe.

elena notices that if she takes the number in the tomatoes column and divides it by the corresponding number in the onions column, she always gets the same result.
what is the meaning of the number that elena has calculated?

onions (oz.)	tomatoes (oz.)
4	32
6	48

1. a restaurant is offering 2 specials: 10 burritos for $12, or 6 burritos for $7.50. noah needs 60 burritos for his party. should he buy 6 orders of the 10-burrito special or 10 orders of the 6-burrito special? explain your reasoning.

Explanation:

Problem 1

Step1: Calculate distance for $\frac{1}{2}$ hour

Use the formula \(d = s\times t\) (distance = speed×time). Here \(s = 55\) mph and \(t=\frac{1}{2}\) hr.
\(d=55\times\frac{1}{2}=\frac{55}{1}\times\frac{1}{2}=\frac{55}{2}=27.5\) mi.

Step2: Calculate distance for \(1\frac{1}{2}\) hour

First, convert \(1\frac{1}{2}\) to an improper fraction: \(1\frac{1}{2}=\frac{3}{2}\). Then use \(d = s\times t\) with \(s = 55\) mph and \(t=\frac{3}{2}\) hr.
\(d = 55\times\frac{3}{2}=\frac{55\times3}{2}=\frac{165}{2}=82.5\) mi.

Step3: Calculate time for 110 miles

Use the formula \(t=\frac{d}{s}\). Here \(d = 110\) mi and \(s = 55\) mph.
\(t=\frac{110}{55}=2\) hr.

We calculate \(\frac{16}{2}=8\), \(\frac{32}{4} = 8\), \(\frac{48}{6}=8\). In a ratio relationship \(y = kx\) (where \(y\) is tomatoes, \(x\) is onions), \(k=\frac{y}{x}\). This \(k\) represents the constant of proportionality. It means for every 1 ounce of onions, there are 8 ounces of tomatoes in the salsa recipe.

Step1: Calculate cost for 6 orders of 10 - burrito special

For the 10 - burrito special (\(10\) burritos for \(\$12\)):
If Noah buys \(6\) orders, the number of burritos \(n=6\times10 = 60\) (which is what he needs).
The cost \(C_1=6\times12=\$72\).

Step2: Calculate cost for 10 orders of 6 - burrito special

For the 6 - burrito special (\(6\) burritos for \(\$7.50\)):
If Noah buys \(10\) orders, the number of burritos \(n = 10\times6=60\).
The cost \(C_2=10\times7.50=\$75\).

Answer:

Time (hr.)	Distance (mi.)	Speed (mph)
\(\frac{1}{2}\)	\(27.5\)	\(55\)
\(1\frac{1}{2}\)	\(82.5\)	\(55\)
\(2\)	\(110\)	\(55\)

Problem 2