Creating Equations
Patrick has saved $600 to buy British pounds and euros for a school trip to Europe. On the day that he goes to buy the currency, one pound costs $2 and one euro costs $1.50. Create an equation to represent this linear relation and identify your variables.
Let x represent the pounds that Patrick buys. Let y represent the euros that he buys.
2x + 1.50y = 600
Joe downloads music to his MP3 player from a site that charges $9.95 per month plus $0.55 for each song. Joe has budgeted $40 per month to spend on music downloads. Determine the maximum number of songs that Joe can download each month.
C = 9.95 + 0.55n
40 = 9.95 + 0.55n
54.6 = n
Can download a maximum of 54 songs.
Is the ordered pair, (10, 0), a point on the graph of 2x + 4y = 20?
Yes!
Judy is considering a sales position. Sam’s store offers $1600/month plus 2.5% commission on sales. Represent Sam’s offer by creating a linear equation. Hint: remember to also identify and define your variables.
Let x represent her sales in dollars. Let y represent her earnings in dollars
y = 1600 + 0.025x
Ben’s Bikes rents racing bikes for $25/day and mountain bikes for $30/day. Yesterday’s rental charges were $3450. Determine the greatest number of racing bikes that could have been rented.
138 racing bikes
Graph: y = 4x + 5
Graph needs:
--> y - intercept of 5
--> Slope of 4: Rise up by 4, run to the right by 2
--> Connect your dots
--> Label your line
Define suitable variables for each situation, and write an equation.
Caroline earns $15/h at her day job and $11/h at her evening job. Last week, she earned $540.
Let x represent number of hours worked at her day job. Let y represent number of hours worked at her evening job.
540 = 15x + 11y
Hank sells furniture and earns $280/week plus 4% commission. a) Determine the sales that Hank needs to make to meet his weekly budget requirement of $900
$15, 500
Solve the linear system by graphing.
x + y = 3
x - y = 7
Define suitable variables for the situation, and write an equation.
Joe downloads music to his MP3 player from a site that charges $9.95 per month plus $0.55 for each song.
Let n represent the number of songs and let C represent the cost.
C = 9.95 + 0.55n
. The Perfect Paving Company charges $10 per square foot to install interlocking paving stones, as well as a $40 delivery feet. Determine the greatest area that Andrew can pave for $3500.
346 square feet.
Define suitable variables for the situation, and write an equation.
Abigail is planning to fly to Paris and then travel through Switzerland and Austria to Italy by train. On the day that she goes to buy the foreign currencies she needs, one euro costs $1.40 and one Swiss franc costs $0.90. Abigail has $630.
Let x represent euros and y represent swiss franc.
1.40x + 0.90y = 630
Prices for cherries and peaches in July of one year are listed at the left. What is the maximum number of kilograms of cherries you can buy for $15? Round your answer to two decimals.
Price per kilogram: cherries $10.98 and peaches $2.18
10.98c + 2.18p = 15
when p = 0
c = 1.388
c = 1.39 kilograms