Sergio is making punch for a school party. The recipe he is using calls for 3 cups of fruit juice to make 7 cups of punch. He made a ratio table to help him determine how much fruit juice he will need. Sergio thinks he will need 90 cups of fruit juice to make 210 cups of punch. Explain his method.
17 gr6
Sergio is using a ratio table to determine how much fruit juice he will need to make a certain amount of punch.
In the ratio table, he writes down the amounts of fruit juice and punch in each row.
For the first row, he writes down 3 cups of fruit juice and 7 cups of punch, based on the recipe.
To figure out how much fruit juice he will need to make 210 cups of punch, Sergio will use proportions.
He sets up a proportion using the information from the first row of the table:
3 cups of fruit juice / 7 cups of punch = 90 cups of fruit juice / 210 cups of punch
To solve the proportion, Sergio uses cross-multiplication:
(3 cups of fruit juice) * (210 cups of punch) = (7 cups of punch) * (90 cups of fruit juice)
This gives him:
630 cups of fruit juice = 630 cups of fruit juice
Since the equation is true, Sergio's method is correct. He will need 90 cups of fruit juice to make 210 cups of punch.
To explain Sergio's method, we need to understand the concept of ratios and how he used a ratio table to determine the amount of fruit juice needed.
In this case, Sergio is making punch using a specific recipe that requires a certain ratio of fruit juice to punch. The recipe states that 3 cups of fruit juice are needed to make 7 cups of punch. This means that for every 3 cups of fruit juice, he will get 7 cups of punch.
To determine how much fruit juice Sergio will need to make a different amount of punch, he uses the concept of proportions. A proportion is an equation that states that two ratios are equal.
In this case, Sergio wants to find out how much fruit juice he will need to make 210 cups of punch. He sets up a ratio table to help him solve this problem.
First, he writes down the known ratio - 3 cups of fruit juice to 7 cups of punch - in the first row of the table:
Fruit Juice : Punch
3 cups : 7 cups
Next, he sets up a proportion by dividing both sides of the ratio table by 7 (the number of cups of punch):
Fruit Juice : Punch
3 cups : 7 cups
3/7 cups : 7/7 cups
Simplifying the ratios gives:
Fruit Juice : Punch
3/7 cups : 1 cup
Now Sergio knows that for every 3/7 cups of fruit juice, he will get 1 cup of punch.
To determine how much fruit juice he will need for 210 cups of punch, Sergio sets up another proportion with the information given:
Fruit Juice : Punch
3/7 cups : 1 cup
x cups : 210 cups
To solve for x (the number of cups of fruit juice), Sergio cross-multiplies:
(3/7) * 210 = 90 cups
According to Sergio's method, he believes that he will need 90 cups of fruit juice to make 210 cups of punch.
I used a proportion and got the same answer.
3/7 = x/210