Question

The table below shows the amount of lemon juice and sugar needed to make three different-sized batches of lemonade using the same recipe. Lemon juice ( mL mLstart text, m, L, end text) Sugar ( g gstart text, g, end text) Batch A 500 500500 200 200200 Batch B 750 750750 300 300300 Batch C 1500 15001500 600 600600 Write an equation to describe the relationship between j jj, the amount of lemon juice in mL mLstart text, m, L, end text, and s ss, the amount of sugar in g gstart text, g, end text.

Answer 1

Answer:

The equation is:

        $j/g=5/2$

Or, what is equivalent:

        $j=5g/2$

Explanation:

This is the table that shows the amount of lemon juice and sugar needed to make three different-sized batches of lemonade using the same recipe:

                        Lemon juice (mL)       Sugar (g)

Batch A               500                            200

Batch B                750                            300

Batch C              1500                            600

You need to write an equation to describe the relationship between j, the amount of lemon juice in mL and s, the amount of sugar in g.

Calculate some ratios, to determine the kind of relation between the amount of juice and the amount of sugar in the recipe.

• Batch A: lemon juice / sugar = 500 / 200 = 5/2

• Batch B: lemon juice / sugar = 750/300 = 5/2

• Batch C:  lemon juice / sugar = 1500/600 = 5/2

Hence, the amount of juice, j, and the amound of sugar, s, are proportional and the constant of proportionality is 5/2. From this, the equation is:

        $j/g=5/2$

Or, what is equivalent (solving for j):

        $j=5g/2$