1.8 Mixture Word Problems
Today’s Date:
9/13/11
Notes on Handout
Mixture
Amount • $/each = Total $
Create a table:
Amt
$/ea
THING 1
THING 2
Mixture
Multiply
Amt = kg, pounds, # of hrs
$/ea = $ ‘per’, ‘an’, ‘a’, each
=
Total $
Add
+
=
Get eqtn from
this column
total spent
Examples
a) Define variable b) Write eqtn. c) Solve
1) Les spent $4.40 for several pencils costing 10 cents each and some
notebooks costing 80 cents each. He bought 8 more pencils than
notebooks. How many notebooks did he buy?
=
Amt
$/ea
Pencils
x +8
10
10(x + 8)
Notebooks
x
80
80x
TOTAL (Mix)
a) x = # of notebooks
b) 10(x + 8) + 80x = 440
10x + 80 + 80x = 440
90x + 80 = 440
90x = 360
Total $
440
+
=
x=4
c) 4 notebooks
Examples
a) Define variable b) Write eqtn. c) Solve
2) Susan makes $3 an hour working after school and $4 an hour
working on Saturdays. Last week she worked a total of 12 hours and
made $42.50. How many hours did she work on Saturday?
=
Amt (# of hrs)
$/hr
After school
12 – x
3
3(12 – x)
Saturday
x
4
4x
TOTAL
12
a) x = # of hrs on Sat
b) 3(12 – x) + 4x = 42.50
36 – 3x + 4x = 42.50
36 + x = 42.50
x = 6.50
Total $
42.50
+
=
# hrs aft sch + # hrs Sat = Total # hrs
# hrs aft sch = Total # hrs – # hrs Sat
c) 6.5 hours
amt of almonds
Examples
a) Define variable b) Write eqtn. c) Solve
3) A company sells cashews that cost $3.50 per pound and almonds
that cost $3.00 per pound. How many kg. of almonds should be mixed
in order to get a mixture that is 10 pounds and costs $3.40 per pound?
=
Amt
$/ea
Cashews
10 – x
3.50
3.50(10 – x)
Almonds
x
3.00
3.00x
Mix
10
a) x = amt of almonds
Total $
+
=
3.40
10(3.40)
amt cashews + amt almonds = amt mix
amt cashews = amt mix – amt almonds
b) 3.50(10 – x) + 3.00x = 10(3.40)
35 – 3.50x + 3.00x = 34
35 – .50x = 34
– .50x = –1
c)
x = 2 pounds
amt of cashews
Examples
a) Define variable b) Write eqtn. c) Solve
4) The Nut House sells walnuts for $4 a pound and cashews for $7 a
pound. How many pounds of cashews should be mixed with 10 pounds
of walnuts to obtain a mixture that sells for $5.50 a pound?
=
Amt
$/ea
Walnuts
10
4
10(4)
Cashews
x
7
7x
Mix
x + 10
5.50
5.50(x + 10)
a) x = amt of cashews
b) 10(4) + 7x = 5.50(x + 10)
40 + 7x = 5.50x + 55
40 + 1.50x = 55
1.50x = 15
Total $
+
=
amt walnuts + amt cashews = amt mix
c)
x = 10 pounds
Homework
#9 Plowed Field WS