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Solve algebraic equations and practical problems using substitution, elimination, and simplification methods. Determine unknown values and quantities based on given information and mathematical expressions. Enhance your math skills with these exercises!
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solve by substitution 2x – y = -9 3x – 8y = -7 (-5, -1)
Simplify • a) (4x3y5)3
A caterer is planning a party for 232 people. The customer has £808 to spend. A £32 pan of pasta feeds 8 people and a £36 sandwich tray feeds 12 people. How many pans of pasta and how many sandwich trays should the caterer make? p = no. of pans of pasta w = no. of trays of sandwiches p = 14 w = 10 32p + 36w = 808 8p + 12w = 232 14 pans of pasta 10 sandwich trays
Solve for x: 5(x + 2) – 2(3 – 2x) = 3
Solve for x: x(2x + 1) – 2(x + 1) = 2x(x – 1) x = 2
The bill for 3 Big Macs and 2 Cokes is 20 CHF. The bill for 7 Big Macs and 8 Cokes is 55 CHF. What would be the bill for 2 Big Macs and 1 Coke? b = cost of 1 Big Mac c = cost of 1 Coke 3b + 2c = 20 7b + 8c = 55 b = 5 CHF c = 2.5 CHF 2 Big Macs and 1 Coke would cost 12.50 CHF.
Simplify a) 7-1 + 70
solve by substitution 5x – y = -11 4x + 12y = 4 (-2, 1)
Travis collects only 50-cent and $1 coins. His collection consists of 43 coins and their total value is $35. How many of each coin type does he have? He has 16 50¢ coins and 27 $1 coins
solve by elimination 2x + 7y = 2 3x + 5y = -8 (-6, 2)
If p = 4, q = -2 and r = 3 find the value of 5r – 4q 23
George is 10 years older than Jane. Three years ago Jane was ¾ as old as George. How old is George now? George is 43 years old.
Write without brackets or negative exponents a) (2a)-1 b) ab-1
Write as powers of 2, 3, or 5 =3-3x =5-2 =2-2
Solve for x. 4x = 8
solve by elimination 3x + 2y = 22 9x – 8y = -4 (4, 5)
Your family is planning a 10 day trip to California. You estimate that it will cost $480 per day in Los Angeles and $380 per day in San Diego. Your total budget for the 10 days is $4200. How many days should you spend in each location? a = no. of days in Los Angeles d = no. of days in San Diego a = 4 d = 6 a + d = 10 480a + 380d = 4200 4 days in Los Angeles 6 days in San Diego