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 -----> 2a = 700 - 300 -----> 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

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