Question

Cafeteria A has 7 packs of granola bars and 12 loose granola bars. Cafeteria B
has 3 packs of granola bars and 84 loose granola bars. If the cafeterias have the
same number of granola bars, how many are in each pack?
granola bar

Answer 1

Cafeteria A has 7 packs of granola bars and 12 loose granola bars. Cafeteria B has 3 packs of granola bars and 84 loose granola bars. If the cafeterias have the same number of granola bars, each package has 18 granola bars.

A linear equation is an algebraic equation of the form y=mx+b. regarding best a consistent and a primary-order (linear) term, where m is the slope and b is the y-intercept. every now and then, the above is known as a "linear equation of two variables," wherein y and x are the variables.

We can find the number of granola bars in each pack using the liner equation.

First, form the equation

Let "$x$" be the total number of granola bars that each pack of granola has.

Let "$y$" be the total amount of granola bars that each cafeteria has.

Cafeteria A: $7x + 12 = y$

Cafeteria B: $3x + 84 = y$

Then, since both the equations are solved $y$, we may take the argument at the left side of the equal sign from both equations and equal them.  $7x + 12 = 3x + 84$

Find the value of $x$

$7x + 12 = 3x + 84$

$7x-3x = 84 - 12$ ( Subtract $3x$ and $12$ from both sides. )

$4x = 72$ ( Simplify by solving the subtraction. )

$\frac{4x}{4}=\frac{72}{4}$ ( Divide both sides by 4. )

$x=18$

Now, substitute the value of $x$ by $x$ on any of the equations.

$y=7(18)+12$

$y=138$

If a system of linear equations was created, where 2 equations gave the number of granola bars that each cafeteria has, then the $x$ value obtained when the system was solved, indicates the number of granola bars that each cafeteria has in each package. Each package has 18 granola bars.

Learn more about linear equations here brainly.com/question/2030026

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