<< Chapter < Page Chapter >> Page >

Translate to a system of equations and solve:

Laura owes $18,000 on her student loans. The interest rate on the bank loan is 2.5% and the interest rate on the federal loan is 6.9 %. The total amount of interest she paid last year was $1,066. What was the principal for each loan?

The principal amount for the bank loan was $4,000. The principal amount for the federal loan was $14,000.

Got questions? Get instant answers now!

Translate to a system of equations and solve:

Jill’s Sandwich Shoppe owes $65,200 on two business loans, one at 4.5% interest and the other at 7.2% interest. The total amount of interest owed last year was $3,582. What was the principal for each loan?

The principal amount for was $41,200 at 4.5%. The principal amount was, $24,000 at 7.2%.

Got questions? Get instant answers now!

Access these online resources for additional instruction and practice with solving application problems with systems of linear equations.

Key concepts

  • Table for coin and mixture applications
    This table is mostly blank. It has four columns and four rows. The last row is labeled “Total.” The first row labels each column as “Type,” and “Number times Value = Total Value.”
  • Table for concentration applications
    This table is mostly blank. It has four columns and four rows. The last row is labeled “Total.” The first row labels each column as “Type,” and “Number of units times Concentration = Amount.”
  • Table for interest applications
    This table is mostly blank. It has five columns and four rows. The last row is labeled “Total.” The first row labels each column as “Type,” and “Principal times Rate times Time = Interest”

Practice makes perfect

Solve Mixture Applications

In the following exercises, translate to a system of equations and solve.

Tickets to a Broadway show cost $35 for adults and $15 for children. The total receipts for 1650 tickets at one performance were $47,150. How many adult and how many child tickets were sold?

There 1120 adult tickets and 530 child tickets sold.

Got questions? Get instant answers now!

Tickets for a show are $70 for adults and $50 for children. One evening performance had a total of 300 tickets sold and the receipts totaled $17,200. How many adult and how many child tickets were sold?

Got questions? Get instant answers now!

Tickets for a train cost $10 for children and $22 for adults. Josie paid $1,200 for a total of 72 tickets. How many children’s tickets and how many adult tickets did Josie buy?

Josie bought 40 adult tickets and 32 children tickets.

Got questions? Get instant answers now!

Tickets for a baseball game are $69 for Main Level seats and $39 for Terrace Level seats. A group of sixteen friends went to the game and spent a total of $804 for the tickets. How many of Main Level and how many Terrace Level tickets did they buy?

Got questions? Get instant answers now!

Tickets for a dance recital cost $15 for adults and $7 for children. The dance company sold 253 tickets and the total receipts were $2,771. How many adult tickets and how many child tickets were sold?

There were 125 adult tickets and 128 children tickets sold.

Got questions? Get instant answers now!

Tickets for the community fair cost $12 for adults and $5 dollars for children. On the first day of the fair, 312 tickets were sold for a total of $2,204. How many adult tickets and how many child tickets were sold?

Got questions? Get instant answers now!

Brandon has a cup of quarters and dimes with a total value of $3.80. The number of quarters is four less than twice the number of quarters. How many quarters and how many dimes does Brandon have?

Brandon has 12 quarters and 8 dimes.

Got questions? Get instant answers now!

Sherri saves nickels and dimes in a coin purse for her daughter. The total value of the coins in the purse is $0.95. The number of nickels is two less than five times the number of dimes. How many nickels and how many dimes are in the coin purse?

Got questions? Get instant answers now!

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask