The number of sticks of gum varies directly as the number of packages. There are 36 sticks of gum in 2 packages. Suppose you have 5 packages of gum. Write and solve a direct variation equation to determine how many sticks you have.
Answer (3)
36 x 2 = 72
36 divide by 2 = 18
72+18=90
90 is the answer
To determine how many sticks of gum are in 5 packages, you first find the constant of variation (18 sticks per package) from the given information (36 sticks in 2 packages). Then, you apply the direct variation formula to calculate the total number of sticks (90 sticks) for 5 packages.
If the number of sticks of gum varies directly with the number of packages, it means that if you have more packages, you'll proportionally have more sticks of gum. This scenario can be described with a direct variation equation, which is of the form y = kx, where y represents the total number of sticks of gum, x is the number of packages, and k is the constant of variation. The question states there are 36 sticks of gum in 2 packages, so we can use this information to find k.
First, let's find the constant of variation:
k = y / x = 36 sticks / 2 packages = 18 sticks per package
Now that we have the constant, we can write the direct variation equation as:
y = 18x
To find out how many sticks are in 5 packages:
y = 18 * 5 = 90 sticks of gum
Therefore, if you have 5 packages of gum, you will have 90 sticks of gum.
The number of sticks of gum varies directly with the number of packages. Using the constant of variation from the given data, we found that in 5 packages, there are 90 sticks of gum. The direct variation equation is g = 18p.
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