Question

1 pax wants to make fruit punch for a party using the recipe below. fruit punch 1.25 l orange juice 2.5 l cranberry juice 1 l ginger ale he will make three times the amount of fruit punch listed in the recipe. what is the total amount of fruit punch, in liters, that pax will make? a 4.53 b 4.75 c 12.90 d 14.25 2 what is the value of the expression below? \\( 3\frac{1}{4} \\) \\( -1\frac{7}{8} \\) a \\( 1\frac{1}{4} \\) b \\( 1\frac{3}{8} \\) c \\( 2\frac{3}{8} \\) d \\( 3\frac{1}{2} \\)

Explanation:

Question 1

Step1: Calculate the total for one recipe

First, find the total volume of the fruit punch for one recipe by adding the volumes of orange juice, cranberry juice, and ginger ale.
The volume of orange juice is \(1.25\) L, cranberry juice is \(2.5\) L, and ginger ale is \(1\) L. So the total for one recipe is \(1.25 + 2.5+ 1\).
\(1.25+2.5 = 3.75\), then \(3.75 + 1=4.75\) L for one recipe.

Step2: Calculate the total for three recipes

Since Pax is making three times the amount of the recipe, we multiply the total for one recipe by 3.
So \(4.75\times3\).
\(4\times3 = 12\), \(0.75\times3 = 2.25\), then \(12 + 2.25 = 14.25\) L.

Step1: Convert mixed numbers to improper fractions

First, convert \(3\frac{1}{4}\) and \(1\frac{7}{8}\) to improper fractions.
For \(3\frac{1}{4}\), we have \(3\frac{1}{4}=\frac{3\times4 + 1}{4}=\frac{13}{4}\).
For \(1\frac{7}{8}\), we have \(1\frac{7}{8}=\frac{1\times8+7}{8}=\frac{15}{8}\).

Step2: Find a common denominator

The common denominator of 4 and 8 is 8. So convert \(\frac{13}{4}\) to eighths: \(\frac{13}{4}=\frac{13\times2}{4\times2}=\frac{26}{8}\).

Step3: Subtract the fractions

Now subtract \(\frac{15}{8}\) from \(\frac{26}{8}\): \(\frac{26}{8}-\frac{15}{8}=\frac{26 - 15}{8}=\frac{11}{8}\).

Step4: Convert back to mixed number

Convert \(\frac{11}{8}\) to a mixed number: \(11\div8 = 1\) with a remainder of 3, so \(\frac{11}{8}=1\frac{3}{8}\).

Answer:

D. 14.25

Question 2