Question

A recipe calls for 3 1/2 teaspoons of mustard​ seeds, 4 cups of tomato​ sauce, and

9 3/4 cups of beans. You use 2 2/3 cups of tomato sauce. How many teaspoons of mustard seeds do you​ need? How many cups of beans do you​ need?

Answer 1

For a recipe call,

Number of teaspoons of mustard seeds =
`3(1)/(2) =(7)/(2)`

Number of cups of tomato sauce = 4

Number of cups of beans =
`9(3)/(4) =(39)/(4)`

For 4 cups of tomato sauce, the number of teaspoons of mustard seeds needed =
`(7)/(2)`

For 1 cup of tomato sauce, the number of teaspoons of mustard seeds needed =
`(7)/(8)`

For
`2(2)/(3) =(8)/(3)` cups of tomato sauce, the number of teaspoons of mustard seeds needed =
`(7)/(8) ((8)/(3) )`

`=(7)/(3)=2 (1)/(3)`

Hence, for
`2(2)/(3)` cups of tomato sauce, the number of teaspoons of mustard seeds needed is
`2(1)/(3)`.

For 4 cups of tomato sauce, the number of cups of beans needed =
`(39)/(4)`

For 1 cup of tomato sauce, the number of cups of beans needed =
`(39)/(16)`

For
`2(2)/(3) =(8)/(3)` cups of tomato sauce, the number of cups of beans needed =
`(39)/(16) ((8)/(3) )`

`=(13)/(2)=6 (1)/(2)`

Hence, for
`2(2)/(3)` cups of tomato sauce, the number of cups of beans needed is
`6(1)/(2)`.