Create Systems Worksheets Grade 9

1. A technology startup is analyzing two different revenue models for their new app. Model X follows a linear growth pattern: R(x) = 25x + 500, where x represents months after launch and R(x) is revenue in dollars. Model Y follows a quadratic growth pattern: R(x) = -x² + 50x + 400. After how many months will both models predict the same revenue, and what will that revenue be?
2. Matiu is analyzing two different investment plans for his savings. Plan A offers a fixed annual return of $120 plus 4% simple interest on the principal amount invested. Plan B offers a fixed annual return of $80 plus 6% simple interest on the same principal amount. Matiu wants to know what principal amount would make both plans yield the same total annual return, and what that total annual return would be. Write a system of equations to represent this situation and solve for the principal amount and the total annual return.
3. A technology startup is analyzing two different revenue models for their new app. Model A generates revenue according to the function R(x) = 2x² + 50x, where x is the number of premium subscribers in hundreds. Model B follows R(x) = -x² + 120x + 800. The company wants to know at what subscriber count both models predict the same revenue, and what that revenue will be. Write and solve a system of equations to answer this question.

…and 3 more problems

1. Emma is analyzing two different investment plans for her savings. Plan A offers a fixed annual interest of $15 plus 5% of the amount invested. Plan B offers a fixed annual interest of $25 plus 3% of the amount invested. At what investment amount will both plans yield the same total annual interest, and what will that interest be? Write a system of equations to model this situation and solve.
2. A theater sells tickets for $12 for adults and $8 for children. For a particular show, the theater sold 120 tickets and collected $1240. How many adult tickets were sold?
3. Matiu is selling two types of handmade crafts at a market. He sold 8 of type A and 6 of type B for a total of $142. Type A sells for $4 more than type B. Write a system of equations to represent this situation.

…and 4 more problems

1. Matiu is selling two types of handmade candles. The large candles sell for $18 each and the small candles sell for $12 each. In one day, he sold 25 candles and collected $390. Write a system of equations to represent this situation, using L for large candles and S for small candles.
2. Olivia runs a small business that produces custom notebooks. She has two production methods. Method A uses a machine with a fixed monthly cost of $75 and a material cost of $3 per notebook. Method B uses handcrafting with a fixed monthly cost of $45 and a material cost of $5 per notebook. Write a system of equations to represent the total monthly cost for each method in terms of the number of notebooks produced. Determine the number of notebooks for which both methods have the same total monthly cost, and what that cost is.
3. Sophia is selling two types of handmade candles. The small candles sell for $6 each and the large candles sell for $11 each. Yesterday she sold 16 candles total and made $156. Write a system of equations to represent this situation, using s for small candles and l for large candles.

…and 4 more problems