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Warm–up #21. Solve2. Solve 3. Solve for R:
Warm–up #2 Solutions1. SolveFor a fraction to = 0, ONLY the numerator needs to = 0 because
3 – 2x = 0 – 2x = –3 x =
Warm–up #2 Solutions2. Solve x + 5 = 3x – 2 or x + 5 = –(3x – 2)–2x = –7 or x + 5 = –3x + 2 4x = –3x = or x = Nope!Check for extraneous solutions!
Warm–up #2 Solutions3. Solve for R:A = )SA = rS + RSA – rS = RS Or
Homework LogFri
10/2
Lesson 2 – 2
Learning Objective: To solve number & investment problems
Hw: #203 Pg. 110 # 1–6, 9–14
10/2/15 Lesson 2 – 2 Number & Investment Problems Day 1
Advanced Math/Trig
Learning Objective
To solve number problems
To solve investment problems
x x+1 x+2
Consecutive Integers
Consecutive Integers:Use: x, x + 1, x + 2, …
+1+1
x x+2 x+4
Consecutive Odd Integers:
Use: x, x + 2, x + 4, …
+2 +2
x x+2 x+4
Consecutive Even Integers:
Use: x, x + 2, x + 4, …
+2 +2
6
SAME!
Consecutive Integers1. Find 2 consecutive positive even integers such that the difference of their squares is 52.1st # = x 2nd # = x+ 2(2nd #)2 – (1st #)2 = 52 (x + 2)2 – (x)2 = 52x2 + 4x + 4 – x2 = 52
4x + 4 = 524x = 48 x = 12 12 & 14
Two-digit NumbersTwo Digit # 23
tens digit units digit2 320 + 3
to get 23!!
Three-digit NumbersThree Digit # 215hundreds digit tens digit units digit
2 1 5200 + 10 + 5
to get 215!
2. The sum of the digits in a 2-digit number is 5. If the digits are reversed, the new number is 9 more than the original number. What is the original number?
Original number: 10x + (5
– x)
New number: 10(5 – x) + x
10x + (5 – x) = 10(5 – x)
+ x
10x + 5 – x + 9 = 50 – 10x
+ x
9x + 14 = –9x + 50
18x = 36
x = 2
Orig # = 23
5x x
5 x x + 9
x = 25 – x = 3
Simple Interest
I = interest earned
p = principal
r = rate %
decimal
t = time (in years)
I prt
Simple Interest3. Part of $9000 is to be invested at 12% and the remainder at 8%. How much should be invested at each rate to yield an annual interest income of $860.
Principal rate time Interest
Inv 1
Inv 2
Total 9000
x9000 – x
.12.08
11
• • =.12x
.08(9000 – x)860
equation!.12x + .08(9000 – x) = 860
.12x + .08(9000 – x) = 860 .12x + 720 – .08x = 860 .04x = 140 x = 3500
9000 – 3500 = 5500
$3500 at 12%$5500 at 8%
Simple Interest #3 cont’d
Consecutive Integers4. Find 3 consecutive odd integers whose sum is 111.1st # = x 2nd # = x + 2 3rd # = x + 4x + (x + 2) + (x + 4) = 1113x + 6 = 1113x = 105x = 3535, 37, 39
Digits of Numbers5. In a three-digit number, the hundreds digit is twice the tens digit and half of the units digits. If the numbers are reversed, the new number is 32 less than twice the original number. Find the original number. Original # 100(2x) + 10(x) + 1(4x)
214xNew # 100(4x) + 10(x) + 1(2x)
412x
Digits of Numbers5. 2(214x) – 32 = 412x
428x – 32 = 412x – 32 = –16xx = 2
Original # 100(2x) + 10(x) + 1(4x) 214x
428
Simple Interest6. Part of $10,000 is to be invested at 15% and the remainder at 9%. How much should be invested at each rate to yield an annual interest income of $1320.
Principal rate time Interest
Inv 1
Inv 2
Total 10000
x10000 – x
.15.09
11
• • =.15x
.09(10000 – x)1320
equation!.15x + .09(10000 – x) = 1320
.15x + .09(10000 – x) = 1320 .15x + 900 – .09x = 1320 .06x = 420 x = 7000
10000 – 7000 = 3000
$7000 at 15%$3000 at 9%
Simple Interest #6 cont’d
Simple Interest7. Jane has four times as much money invested in bonds paying 12% as she does in stocks paying 10%. If her total annual interest income from these investments is $696, how much does she have invested in each? Principal rate time Interest
Bonds
Stocks
Total
4x
x.12.10
11
• • =.48x.1x696
equation!.48x + .1x = 696
.48x + .1x = 696 .58x = 696 x = 1200
4(1200) = 4800
$1200 in stocks$4800 in bonds
Simple Interest #7 cont’d
Ticket Out the Door
In a two-digit number, the units digit is 3 less than twice the tens digit. If the digits are reversed, the new number is 18 more than the original number. Find the original number.
Homework
#203 Pg. 110 #1 – 6, 9 – 14
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