Warm–up #2

Warm–up #2 Solutions

Homework Log Fri 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 x x+2 x+4 Consecutive Odd Integers: Use: x, x + 2, x + 4, … +2 x x+2 x+4 Consecutive Even Integers: Use: x, x + 2, x + 4, … +2 6 SAME!

Consecutive Integers 1. Find 2 consecutive positive even integers such that the difference of their squares is st # = x2 nd # = x+ 2 (2 nd #) 2 – (1 st #) 2 = 52 (x + 2) 2 – (x) 2 = 52 x 2 + 4x + 4 – x 2 = 52 4x + 4 = 52 4x = 48x = & 14

Two-digit Numbers Two Digit #  23 tens digitunits digit to get 23!!

Three-digit Numbers Three Digit #  215 hundreds digit tens digitunits digit 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 x = 36 x = 2 Orig # = x = 2 5 – x = 3

Simple Interest I = interest earned p = principal r = rate %  decimal t = time (in years)

Simple Interest 3. 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. PrincipalratetimeInterest Inv 1 Inv 2 Total 9000 x 9000 – x =.12x.08(9000 – x) 860 equation!.12x +.08(9000 – x) = 860

.12x –.08x = x = 140 x = – 3500 = 5500 $3500 at 12% $5500 at 8% Simple Interest #3 cont’d

Consecutive Integers 4. Find 3 consecutive odd integers whose sum is st # = x 2 nd # = x rd # = x + 4 x + (x + 2) + (x + 4) = 111 3x + 6 = 111 3x = 105 x = 35 35, 37, 39

Digits of Numbers 5. 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)  214x New #  100(4x) + 10(x) + 1(2x)  412x

Digits of Numbers 5. 2(214x) – 32 = 412x 428x – 32 = 412x – 32 = –16x x = 2 Original #  100(2x) + 10(x) + 1(4x)  214x  428

Simple Interest 6. 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. PrincipalratetimeInterest Inv 1 Inv 2 Total x – x =.15x.09(10000 – x) 1320 equation!.15x +.09(10000 – x) = 1320

.15x –.09x = x = 420 x = – 7000 = 3000 $7000 at 15% $3000 at 9% Simple Interest #6 cont’d

Simple Interest 7. 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? PrincipalratetimeInterest Bonds Stocks Total 4x x =.48x.1x 696 equation!.48x +.1x = 696

.58x = 696 x = (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