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An order of trail mix and granola weighs 21 pounds and costs $51.

Trail mix: $3.00 per pound
Granola: $2.00 per pound
How many pounds of trail mix and granola are in this order?
Start by writing an expression to represent the cost of t pounds of trail mix. Keep in mind that 1 pound of trail mix costs $3.00
Cost of t
pounds of
trail mix
+
Cost of g pounds of granola
=
Total Cost
+
?
=
?
Great job!
Now, add an expression to represent the cost of g pounds of granola. Keep in mind that 1 pound of granola costs $2.00.
Cost of
t
pounds of trail mix
+
Cost
of
g
pounds of
granola
=
Total Cost
3t
+
=
?

1 answer

Let's write the expressions step by step.

  1. Cost of \( t \) pounds of trail mix: Since 1 pound of trail mix costs $3.00, the cost of \( t \) pounds of trail mix is given by: \[ \text{Cost of } t \text{ pounds of trail mix} = 3t \]

  2. Cost of \( g \) pounds of granola: Since 1 pound of granola costs $2.00, the cost of \( g \) pounds of granola is given by: \[ \text{Cost of } g \text{ pounds of granola} = 2g \]

Now, we can combine these costs into a single equation that represents the total cost: \[ 3t + 2g = 51 \]

Now, let's also set up the equation based on the total weight of the order. We know that the total weight of trail mix and granola is 21 pounds. Therefore, we can write: \[ t + g = 21 \]

We now have a system of equations:

  1. \( 3t + 2g = 51 \)
  2. \( t + g = 21 \)

From these two equations, we can solve for the values of \( t \) (pounds of trail mix) and \( g \) (pounds of granola).

Let's solve these equations step-by-step.

Step 1: Solve the second equation for \( g \):

From the second equation: \[ g = 21 - t \]

Step 2: Substitute \( g \) into the first equation:

Now substitute \( g \) into the first equation: \[ 3t + 2(21 - t) = 51 \]

Step 3: Simplify and solve for \( t \):

\[ 3t + 42 - 2t = 51 \] \[ t + 42 = 51 \] \[ t = 51 - 42 \] \[ t = 9 \]

Step 4: Use \( t \) to find \( g \):

Now substitute \( t = 9 \) back into the equation for \( g \): \[ g = 21 - t = 21 - 9 = 12 \]

Final Result:

The order consists of:

  • 9 pounds of trail mix
  • 12 pounds of granola

So the final solution is:

  • \( t = 9 \)
  • \( g = 12 \)