Systems and Equations Essay

759 WordsMar 30, 20154 Pages
MA1210 Module 4 Systems of Equations and Matrices 10/13/14 Pamela 1. 2a + b = 700 a + 4b = 1400 -2a -8b = -2800 2a - 2a + b - 8b = 700 – 2800 Combining like terms gives us: -7b = -2100 Divide both sides by -7, which gives us: b = 300 We now know that 1 packet of brownies contain 300 calories. To find out the number of calories in 1 packet of apples, simply replace b with 300 in either of our original equations. I will use the first equation, 2a + b = 700: 2a + 300 = 700 -----&gt; 2a = 700 - 300 -----&gt; 2a = 400 Finally, divide both sides by 2, giving us: a = 200 Therefore each packet of apples contains 200 calories and each packet of brownies contains 300 calories. 2. a+b=150, 80a+60b=10000 a = 50 at \$80 for \$4000, b = 100 at \$60 for \$6000 3. 2l + 2w = 300m l + w = 150m, w = 150m-L [2L + (150 - L)] 50 = 12000 100L + 7500 - 50L = 12000 50L = 4500 L = 90m and W = 60m CHECKING our answer \$50 * 240m = \$12,000 4. Let a = no. of adults Let c = no. of children From the given information, we can derive two simple equations The total no. of people a + c = 2000 And the total amt of \$ received 4a + 2c = 6000 Multiply the 1st equation by 2 and subtract from the 2nd equation 4a + 2c = 6000 2a + 2c = 4000 Subtraction eliminates c, find a 2a = 2000 a = 2000/2 a = 1000 adults and 1000 children 5. 4,5,6 x+1=y, x+y=15, x+y=2y 6. \$5--x numbers \$10--y \$15--z x+y=180 5x+10y+15z= 1900 Sum of \$5 and \$15 tickets = twice \$10 x+y= 2y x+y=180 x+y=2y 2y+y=180 3y= 180 y=60, number of \$10 tickets 5x+10y+15z= 1900 5x+10*60+15z=1900 5x+600+15z=1900 5x+15z=1300 /5 x+3z=260 But x+y=120 120+2z=260 2z=260-120 2z=140 z=70 Number of \$15 tickets Balance \$ 5 tickets 7. x + y + z = 7, where x, y, and z