mr. williamson bought 4 boxes of chewy granola bars and 5 boxes of crunchy granola bars. each box contained…

mr. williamson bought 4 boxes of chewy granola bars and 5 boxes of crunchy granola bars. each box contained the same number of granola bars. he took all 72 granola bars to the class picnic. how many granola bars were in each box? let x represent the number of granola bars in each box. step 1: write an equation. step 2: identify and combine like terms. step 3: use the properties of equality and inverse operations to solve the equation.

mr. williamson bought 4 boxes of chewy granola bars and 5 boxes of crunchy granola bars. each box contained the same number of granola bars. he took all 72 granola bars to the class picnic. how many granola bars were in each box? let x represent the number of granola bars in each box. step 1: write an equation. step 2: identify and combine like terms. step 3: use the properties of equality and inverse operations to solve the equation.

Answer

Explanation:

Step1: Write an equation

The number of chewy granola bars is (4x) (since 4 boxes and (x) bars per box) and the number of crunchy granola bars is (5x) (since 5 boxes and (x) bars per box). The total number of granola bars is 72. So the equation is (4x + 5x=72).

Step2: Identify and combine like terms

(4x) and (5x) are like - terms. Using the distributive property (a\times c + b\times c=(a + b)\times c) (here (a = 4), (b = 5), (c=x)), we get ((4 + 5)x=72), which simplifies to (9x=72).

Step3: Use the properties of equality and inverse operations to solve the equation

The inverse operation of multiplication (since (9x) means (9\times x)) is division. Divide both sides of the equation (9x = 72) by 9. So (x=\frac{72}{9}).

Answer:

(x = 8)