Applications of Systems of Linear Equations

i.e. Word Problems!!!

Piggy Bank

• A child has 25 coins in a piggy bank consisting of dimes and quarters. The total value of the coins is $3.70. Find the number of dimes and the number of quarters.

Piggy Bank

• We have two unknowns in this problem,– Let d = – Let q =

• We have two totals we are concerned with,– The total number of ____________– The total amount of ____________

Piggy Bank

• How can we verbally represent the total number of coins?

• How can we algebraically represent the total number of coins?

Piggy Bank

• How can we verbally represent the total amount of money in the piggy bank?

• How can we algebraically represent the total amount of money in the piggy bank?

Piggy Bank

• We have two linear equations – what should we do??

The Chemist

• You are in Chem. lab and in order to pass your lab you need to make 3 gallons of a solution that is 12% acid. To make the required mixture you need to mix two solutions. One solution is 8% acid and another is 18% acid. How many gallons of each acid should be mixed to produce 30 gallons of a solution that is 12% acid?

The Chemist

• We have two unknowns in this problem,– Let x = – Let y =

• We have two totals we are concerned with,– The total volume of ____________– The total volume of ____________

The Chemist

• How can we verbally represent the total volume of solution?

• How can we algebraically represent the total volume of solution?

The Chemist

• How can we verbally represent the total volume of acid?

• How can we algebraically represent the total volume of acid?

The Chemist

• Again we have two linear equations – what should we do???

The Entrepreneur Lavely Inc. has daily fixed costs from salaries, rent, and other

operations of $600. Each widget Lavely Inc makes costs $25 and sells for $45.a.) Determine the cost C of producing x widgets per day.

The Entrepreneur

b.) Determine the revenue R of selling x widgets per day.

The Entrepreneur

c.) Graph the cost and revenue functions – what does the intersection represent?