Math

QuestionDetermine the ratios from the points (2,3), (4,6), (6,9), (8,12). For every \_\_\_ cup(s) of water, \_\_\_ cup(s) of flour. When 8 cups of water, \_\_\_ cups of flour needed.

Studdy Solution

STEP 1

Assumptions1. The points on the graph represent the relationship between the amount of flour and water used in a recipe. . The points are (,3), (4,6), (6,9), (8,12) where the first value in each pair represents the amount of water and the second value represents the amount of flour.
3. The relationship is linear, meaning that the ratio of flour to water is constant.

STEP 2

We need to find the ratio of flour to water. We can do this by dividing the amount of flour by the amount of water for each point on the graph.
Ratio=FlourWaterRatio = \frac{Flour}{Water}

STEP 3

Now, plug in the values for the first point (2,3) to calculate the ratio.
Ratio=32Ratio = \frac{3}{2}

STEP 4

Calculate the ratio for the first point.
Ratio=32=1.Ratio = \frac{3}{2} =1.This means that for every2 cups of water,3 cups of flour are used.

STEP 5

To confirm that the ratio is constant, calculate the ratio for the other points on the graph.
For the point (4,):
Ratio=4=1.5Ratio = \frac{}{4} =1.5For the point (,9):
Ratio=9=1.5Ratio = \frac{9}{} =1.5For the point (8,12):
Ratio=128=1.5Ratio = \frac{12}{8} =1.5As we can see, the ratio is constant for all points on the graph.

STEP 6

Now, we need to express the ratio in terms of the given options for the blanks. The ratio1.5 can be expressed as3 to2. So, for every2 cups of water,3 cups of flour are used.
So, Blank1 =2 and Blank2 =3.

STEP 7

Finally, we need to find the amount of flour needed when cups of water are used. We can do this by multiplying the amount of water by the ratio.
Flour=WatertimesRatioFlour = Water \\times Ratio

STEP 8

Plug in the values for the amount of water and the ratio to calculate the amount of flour.
Flour=8times1.5Flour =8 \\times1.5

STEP 9

Calculate the amount of flour needed.
Flour=8times.5=12Flour =8 \\times.5 =12So, when8 cups of water are used,12 cups of flour are needed.
Blank3 =12.
For every2 cup(s) of water,3 cup(s) of flour are used.When8 cups of water are used,12 cups of flour are needed.

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