3.1+Mixing+Juice+1011

//3.1: MIXING JUICE // **Big Idea: ** Many important practical and mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use and how we should use them.

**Essential question: ** What methods can we use to compare?

**__ 3.1 __** **A. Which recipe will make juice that is the most “orangey”? Explain your answer. ** Mix A is the most ‘orangey’, because Mix A = 40% concentrate or 2 to 5. **B. Which recipe will make juice that is the least “orangey”? Explain your answer. ** Mix B is the last ‘orangey’, because Mix B = 20% concentrate or ¼ (0.25 cups of concentrate per one cup of water). **C. Assume that each camper will get ½ cup of juice. For each recipe, how much concentrate and how much water are needed to make juice for 24 campers? Explain your answer. ** Answer: One half of 240 = 120 (120 cups of juice of 240 of the campers.) <span style="color: black; font-family: 'Century Gothic','sans-serif';">Mix A = 48 cups (0.4 x 120) of concentrate and 72 (0.6 x 120) cups of water. <span style="display: block; line-height: normal; margin: 0in 0in 10pt; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-align: justify;"><span style="color: black; font-family: 'Century Gothic','sans-serif';">Mix B = 24 cups (0.2 x 120) of concentrate and 96 cups (0.8 x 120) of water. <span style="display: block; line-height: normal; margin: 0in 0in 10pt; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-align: justify;"><span style="color: black; font-family: 'Century Gothic','sans-serif';">Mix C = 40 cups (0.33 x 120) of concentrate and 80 cups (0.67 x 120) of water. <span style="display: block; line-height: normal; margin: 0in 0in 10pt; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-align: justify;"><span style="color: black; font-family: 'Century Gothic','sans-serif';">Mix D =45 cups (0.375 x 120) of concentrate and 75 cups (0.625 x 120) of water. ** Follow Up ** ** 1. How did you use ratios in solving Problem 3.1? ** <span style="color: black; font-family: 'Century Gothic','sans-serif'; line-height: normal; margin: 0in 0in 0pt 0.5in;">I used ratios to see which recipe for juice was more or less and then I used those ratios to help me find percentages of the amounts.

**<span style="color: black; font-family: 'Century Gothic','sans-serif';">2. ****<span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 12pt;">For each recipe, how much concentrate and how much water is needed to make 1 cup of juice ** <span style="color: black; font-family: 'Century Gothic','sans-serif'; line-height: normal; margin: 0in 0in 0pt 0.5in; text-indent: -0.25in;">Mix A = 0.4 of orange concentrate and 0.6 water.

<span style="color: black; font-family: 'Century Gothic','sans-serif'; line-height: normal; margin: 0in 0in 0pt 0.5in;">Mix B = 0.2 of orange concentrate and 0.8 water <span style="color: black; font-family: 'Century Gothic','sans-serif'; line-height: normal; margin: 0in 0in 0pt 0.5in;">. <span style="color: black; font-family: 'Century Gothic','sans-serif'; line-height: normal; margin: 0in 0in 0pt 0.5in;">Mix C = 0.33 of orange concentrate and 0.67 water.

<span style="color: black; font-family: 'Century Gothic','sans-serif'; line-height: normal; margin: 0in 0in 10pt 0.5in;">Mix D = 0.375 of orange concentrate and 0.625 water.