# Problem Solving with Linear Equations

• August 27th 2006, 02:09 PM
Dogcop
Problem Solving with Linear Equations
I need help with the following questions:

1. One half my age is 10 years more than one-third my age. How old am I?

2. A maker of an orange drink can purchase her raw materials from two sources.
The first source provides liquid with 6% orange juice, while the second source provides liquid with 3% orange juice. She wishes to make 1 litre of drink with 5% orange juice. Lex x = amount of liquid purchased from the first source.

A. Write the expression for the amount of orange juice from the first supplier, given that x is the amount of liquid

B. Write an expression for the amount of liquid from the second supplier, given that x is the amount of liquid used from the first supplier.

C. Write an expression for the amount of orange juice from the second supplier.

D. Write an equation for the total amount of orange juice of the mixture of the 2 supplies, given that 1 litre of drink is mixed to contain 5% orange juice.

E. How much of the first supplier's liquid should she use?

3. Rachel, the bushwalker, goes on a 4-day journey. She travels a certain distance on the first da, half that distance on the second day, a third that distance on the third day and a fourth of that distance on the fourth day. If the total journey is 50km, how far did she walk on the first day?

Thanks,
Dogcop
• August 27th 2006, 03:57 PM
dan
hi dogcop, i'll start with your first one... if your age is $x$ then your age should be $(1/2)x=(1/3)x +10$

then $(1/3)x - (1/2)x=-10$
$x(1/3 - 1/2 )=-10$
$x =-10/(-1/6)=60$

dan
• August 27th 2006, 04:02 PM
Quick
Quote:

Originally Posted by dan
hi dogcop, i'll start with your first one... if your age is $x$ then your age should be $(1/2)x=(1/3)x +10$

then $(1/2)x - (1/3)x=10$
$x(1/2 - 1/3 )=10$
$x=6$

dan

What dan meant was x=60, which proves it's always a good idea to check your answer...
• August 27th 2006, 04:08 PM
Dogcop
I've manged to figure out the first and third question with help from a friend, but still no clue on the second question
• August 27th 2006, 04:38 PM
dan
Quote:

Originally Posted by Quick
What dan meant was x=60, which proves it's always a good idea to check your answer...

thanks quick:o i made my post so fast I didi'nt find out it was wrong till latter...
• August 27th 2006, 04:52 PM
Jameson
I'll start you out. If x is the amount of juice purchased from the first supplier, than the amount of orange juice is 6% times the amount of juice bought. Thus $A_{fs}(x)=.06x$