Warm–up #3
1. Find two consecutive integers whose
product is 756.
2. If $7000 is invested at 7% per year, how
much additional money needs to be
invested at 14% per year so that the total
annual interest income from the
investments is $1750?
Warm–up #3 Solutions
1. Find two consecutive positive integers
whose product is 210.
1st # = x
2nd # = x + 1
x(x + 1) = 210
x2 + x – 210 = 0
(x + 15)(x – 14) = 0
x = –15, 14
14 & 15
Warm–up #3 Solutions
2. If $7000 is invested at 7% per year, how
much additional money needs to be invested at
14% per year so that the total annual interest
income from the investments is $1750?
Principal
Inv 1
Inv 2
Total
7000
x
7000 + x
•
rate
.07
.14
490 + .14x = 1750
•
time
1
1
=
Interest
7000(.07) = 490
.14x
1750
equation!
Warm–up #3 Solutions
490 + .14x = 1750
.14x = 1260
x = 9000
$9000 at 14%
Homework Log
Tues
Learning Objective:
To solve mixture problems
10/6
Lesson
2–2
Hw: #204 Pg. 111 #17, 18,
21 – 26 all, redo 3, 5, 11
10/6/15 Lesson 2 – 2 Mixture
Problems Day 2
Advanced Math/Trig
Learning Objective

To solve mixture problems
Mixture Solutions
“Pure” Acid = 100%
“Water” = 0%
Tells you it’s
the mix
Mixture
1. A chemist has 16L of a mixture that is
65% acid. How much of an 85% solution
should she add to make a mixture that is 70%
acid?
Amount
Solution 1
Solution 2
Mix
16
x
x + 16
•
%
65
85
70
=
Total
16(65)
85x
70(x + 16)
16(65) + 85x = 70(x + 16)
Mixture Problem #1
cont’d
16(65) + 85x = 70(x + 16)
1040 + 85x = 70x + 1120
15x = 80
x = 5 1 /3 L
Mixture
2. If the popcorn is worth $0.80 a pound &
peanuts are worth $2.50 a pound, how much of
each should go into the mixture for a 1-pound
box that sells for $1.82 per pound?
Amount
Popcorn
Peanuts
Mix
x
1–x
1
•
$/ea
0.80
2.50
1.82
=
Total
.80x
2.50(1 – x)
1.82
.80x + 2.50(1 – x) = 1.82
Mixture Problem #2
cont’d
.80x + 2.50(1 – x) = 1.82
.80x + 2.50 – 2.50x = 1.82
–1.7x = –.68
x = .4
1 – x = .6
.4 lb of popcorn
.6 lb of peanuts
Mixture
3. 4 qt. of an acid solution was mixed with 6
qt of pure water to make an 8% acid solution.
Find the % concentration of the first solution.
Amount
Solution 1
Solution 2
Mix
4
6
10
4x + 0 = 80
•
%
=
x
0
8
Total
4x
0
80
20%
Mixture
4. Hot Peanuts which cost $11/oz are made by
combining peanuts that cost $7/oz with spices
that cost $21/oz. How many oz of peanuts and
spices are needed to make 7oz of Hot Peanuts?
Amount
Peanuts
Spices
Hot Peanuts
x
7–x
7
•
$/ea
7
21
11
7x + 21(7 – x) = 77
=
Total
7x
21(7 – x)
77
Mixture Problem #4
cont’d
7x + 21(7 – x) = 77
7x + 147 – 21x = 77
–14x = –70
x=5
7–x=2
5 oz of peanuts
2 oz of spices
Coin Problems
5. Suppose 21 nickels, dimes, & quarters are
worth $2.45 & there are three times as many
dimes as quarters. How many of each are there?
Amount
Nickels
Dimes
Quarters
Total
21 – 3x – x
3x
x
21
•
$/ea
0.05
0.10
0.25
=
Total
.05(21 – 4x)
.10(3x)
.25x
2.45
.05(21 – 4x) + .10(3x) + .25x = 2.45
Coin Problem #5 cont’d
.05(21 – 4x) + .10(3x) + .25x = 2.45
5(21 – 4x) + 10(3x) + 25x = 245
105 – 20x +30x + 25x = 245
35x = 140
x=4
3x = 12
21 – 4 – 12 = 5
5 Nickels, 12 Dimes, & 4 Quarters
Ticket Out the Door
 Paula
wants to make 15 gal.
of 57% acid solution by
mixing together a 65% acid
solution and a 55% acid
solution. How much of each
solution must she use?
Homework
#204
Pg. 112
17, 18, 21 – 26 all
& RE-DO 3, 5, 11
“Pure” acid  100%
“Water”  0%