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Transcript of $100 $200 $300 $400 $500 $200 $300 $400 $500 Problem Solving Multi-Step Equations Simple and...
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Problem Solving
Multi-Step Equations
Simple and Compound Interest
Multi-Step Inequalities
Transforming Formulas
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Problem Solving for $100
Find 4 consecutive even integers whose sum is 228
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Let x be the smallest of the numbers. Then, the other numbers will be x+2, x+4 and x+6
x + (x+2) + (x+4) + (x+6) = 2284x + 12 = 2284x = 216x = 54. So the other numbers are 56, 58 and 60
Answer
Back
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Problem Solving for $200
An item is on sale for 30% off the original price. The final sale price is $42.65. What was the original price?
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Answer
Back
Let x = the original price of the item. Then:x - 0.3x = $42.650.7x = $42.65x = $60.93
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Problem Solving for $300
Andy puts a certain amount of money into a bank account. When he withdrew the money from the account he had $558.45. If this is 9.5% more than he started with, how much money did he deposit into the account?
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Answer
Back
Let x = the amount of money he started with. Then:
x + 0.095x = $558.45
1.095x = $558.45
x = $510
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Problem Solving for $400
If the perimeter of a rectangle is 64cm and the length is 10cm less than twice the width. What is the length and width of the rectangle?
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P = 2(L+w)let x = the width. Then:2x – 10 = L so,64 = 2(2x – 10 + x)32 = (2x + x – 10)32 = 3x – 1042 = 3x14 = x so, the width = 14 and the length = 2(14) -10 = 28-10 = 18cm
Answer
Back
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Problem Solving for $500
The cost of renting a car is $50 per day plus 15 cents per mile driven. If Amy rented the car for three days and paid a total of $217.50, how many miles did she drive?
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Answer
Back
Let x = the # of miles driven. Then,$217.50 = 50(3) + 0.15x217.50 = 150 + .15x67.50 = .15xx = 450 miles
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Multi-Step Equations for $100
Solve for x:
3x = x/3
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Answer
3x = x/3
9x = x
8x = 0
x = 0Back
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Multi-Step Equations for $200
Solve for C:
7 + 2(3 + C) = 2(3 + 7) + C
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Answer
7 + 2(3 + C) = 2(3 + 7) + C
7 + 6 + 2C = 6 + 14 + C
13 + 2C = 20 + C
2C = 7 + C
C = 7
Back
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Multi-Step Equations for $300
Solve for d:
7.25d + 2d – 5d – 2 = 4d + 3
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Answer
7.25d + 2d – 5d – 2 = 4d + 34.25d – 2 = 4d + 30.25d – 2 = 30.25d = 5d = 20
Back
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Multi-Step Equations for $400
Solve for n.
(1/3)(n + 9) – 5 = 7
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Answer
Back
(1/3)(n + 9) – 5 = 7
(1/3)(n + 9) = 12
n+9 = 36
n = 27
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Multi-Step Equations for $500
Solve for p.
4p – 4 = 2(p+3) – 6(9-p)
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Answer
Back
4p – 4 = 2(p+3) – 6(9-p) 4p – 4 = 2p + 6 – 54 + 6p 4p – 4 = 2p + 6p + 6 – 54 4p – 4 = 8p – 48 -4 = 4p – 48 44 = 4p p = 11
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Multi-Step Inequalities for $100
Solve for x:
x/(3) + 3 > 5
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Answer
x/(3) + 3 > 5x/(3) + 3 - 3 > 5 - 3x/(3) > 2x/(3) * 3 > 2 * 3X > 6
Back
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Multi-Step Inequalities for $200
Solve for x:
-5x + 20 ≤ 10
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Answer
-5x + 20 ≤ 10 -20 -20-5x ≤ -10(-5x)/(-5)≤ (-10)/(-5)X ≥ 2
Back
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Multi-Step Inequalities for $300
Replace the with a number that makes the inequalities equivalent
-3x >
x < -9
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Answer
-3x > (-3x)/(-3) > / (-3)x < /(-3) and x < -9So, /(-3) = -9 /(-3) * -3 = -9 * -3 = 27
Back
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Multi-Step Inequalities for $400
Solve for x:
-(x-6) + 5 - 2x < 8
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Answer-(x-6) + 5 - 2x < 8-(x-6) + 5 - 5 - 2x < 8 – 5-(x-6) - 2x < 3-x + 6 – 2x < 3-3x + 6 < 3-3x + 6 – 6 < 3 – 6-3x < -3(-3x)/(-3) < (-3)/(-3)X > 1
Back
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Multi-Step Inequalities for $500
Solve for x.
10x – 5 - 3x > 3 – (5 - x)
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Answer10x – 5 - 3x > 3 – (5 - x)7x – 5 > 3 – 5 + x7x – 5 > -2 + x7x > 3 + x6x > 3x > 0.5
Back
Check 1: (Substitute it in –> Should be equal)
10(0.5) – 5 – 3(0.5) = 3 – (5 – (0.5))
5 - 5 – 1.5 = 3 - 4.5
-1.5 = -1.5
Check 2: (Pick value that is true)
Let x = 1
10(1) – 5 – 3(1) > 3 – (5 – (1))
10 - 5 – 3 > 3 - 4
2 > -1 => True
Check 3: (Pick value that is false)
Let x = 0
10(0) – 5 – 3(0) = 3 – (5 – (0))
-5 > 3 - 5
-5 > -2 => FALSE
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Transforming Formulas for $100
Solve for x:
y = -2x + 5
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Answer
y = -2x + 5
y - 5 = -2x
y-5 = x
-2
Back
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Transforming Formulas for $200
Solve for m:
n = 4p + 5m
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Answern = 4p + 5mn – 4p = 5m
n – 4p = m
5
Back
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Transforming Formulas for $300
Solve for p:
2t = s/4 – 8p
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Answer
2t = s/4 – 8p
2t – s/4 = -8p
-t + s = p
4 32
Back
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Transforming Formulas for $400
Solve for y:
7y – 3x = 2m
4 2
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Answer
7y – 3x = 2m
4 2
7y – 6x = 8m7y = 8m + 6x y = 8m + 6x
7Back
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Transforming Formulas for $500
Solve for c:
C – 3m + 5 = 2n
2
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Answer
C – 3m + 5 = 2n 2C – 3m = 2n - 5 2C – 3m = 2(2n – 5)C – 3m = 4n – 10C = 4n + 3m – 10
Back
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Simple and Compound Interest for $100
Write the formula for simple interest.
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Answer
I = prt
I: Interest
p: Principal
r: Rate
t: Time
Back
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Simple and Compound Interest for $200
Write the formula for compound interest:
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Answer
B = p(1+r)n
B: Balancep: Principalr: Raten: Number of times interest is
compounded
Back
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Simple and Compound Interest for $300
If Jane put $800 into a bank account which pays 3.25% simple interest annually for 4 years, how much money did she have at the end?
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Answer
I = prtI = 800 * 0.0325 * 4I = 104
Total = p +I = 800 + 104 = $904
Back
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Simple and Compound Interest for $400
Find the balance if $675 is deposited in an account which pays 3.75% interest compounded annually for 4 years.
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AnswerB = p(1+r)n
Compounded Annually:
p = $675
r = 3.75%
n = 4 years
B = 675(1 + .0375)4
B = $782.09
Back
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Simple and Compound Interest for $500
Find the balance if $29,200 is deposited in an account which pays 2.4% interest compounded quarterly for 3 years.
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Answer
Back
B = p(1+r)n
Compounded Quarterly:
p = $29,200
r = 2.4% = .024/4 (quarterly) = .006
n = 3 years * 4 = 12 times
B = 29,200(1 + .006)12
B = $31,373.19