 word problem help? - XP Math - Forums Sign Up FREE! | Sign In | Classroom Setup | Common Core Alignment  XP Math - Forums word problem help? 02-13-2009 #1 milk123   Join Date: Feb 2009 Posts: 3 word problem help? Hi everyone, i'm new here. Seems like a great educational site. Its been a while for me and i really need some help with the formula and explaination. The fuel for a two-cycle motorboat engine is a mixture of gasoline and oil in the ratio of 15 to 1. How many liters of each are in 6.6L of mixture? Fifty kilograms of a cement-sand mixture is 40% sand. How many kilograms of sand must be added for the resulting mixture to be 60% sand? A karat equals 1/24 part of gold in an alloy (for example, 9-karat gold is 9/24 gold). HOw many grams of 9-karat gold must be mixed with 18 karat gold to get 200g of 14-karat gold?  02-13-2009   #2
MAS1   Join Date: Dec 2008
Posts: 249 Mixture Math!

Quote:
 Originally Posted by milk123 Hi everyone, i'm new here. Seems like a great educational site. Its been a while for me and i really need some help with the formula and explaination. The fuel for a two-cycle motorboat engine is a mixture of gasoline and oil in the ratio of 15 to 1. How many liters of each are in 6.6L of mixture? Fifty kilograms of a cement-sand mixture is 40% sand. How many kilograms of sand must be added for the resulting mixture to be 60% sand? A karat equals 1/24 part of gold in an alloy (for example, 9-karat gold is 9/24 gold). HOw many grams of 9-karat gold must be mixed with 18 karat gold to get 200g of 14-karat gold?
1. If the ratio of gasoline to oil in the mixture is 15 to 1, then in a 16 L sample of the mixture there are 15 L of gasoline and 1 L of oil. In other words, 15/16 of the mixture is gasoline, and 1/16 is oil.

So if the total is 6.6L then 15/16 of it is gasoline and 1/16 is oil.
(15/16)*6.6 = 6.1875 L gasoline
(1/16)*6.6 = 0.4125 L oil

2. If 50 kg of a cement-sand mixture is 40% sand then:
(0.40)*50kg = 20 kg sand (S) and (50 - 20) = 30 kg cement (C).

The ratio of sand in the mixture is given by:
S / (S + C).

Therefore if we want 60% sand then we have:
S / (S + C) = 0.60
Since the amount of cement does not change then C = 30 and we have:
S / (S + 30) = 0.60
Solving for S gives S = 45 kg. Since we already have 20 kg of sand, then we need to add 25 kg of sand.

3. 9 karat gold = 9/24 gold
18 karat gold = 18/24 gold
X = grams of 9 karat gold
Y = grams of 18 karat gold

(9/24)*X + (18/24)*Y = (14/24)*200
Also by weight we have the equation:
X + Y = 200

Since we have two equations and two unknowns set them up like:

(9/24)*X + (18/24)*Y = 2800/24
X + Y = 200
Multiplying the bottom equation by 9/24 gives:

(9/24)*X + (18/24)*Y = 2800/24
(9/24)*X + (9/24)* Y = 1800/24

Subtracting the bottom equation from the top gives:

(9/24)*Y = 1000/24. Solving for Y gives:

Y = 1000/9 = 111 1/9 = 111.11 grams of 18 karat gold

Plugging the value for Y back into one of the equations and solving for X gives:

X = 800/9 = 88 8/9 = 88.89 grams of 9 karat gold.

Another way to set up the equations is:

(9/24)*X + (18/24)*Y = (14/24)*200 (Amount of gold in the alloy)
(15/24)*X + (6/24)*Y = (10/24)*200 (Amount of other metal in the alloy).

Hope this helps.  02-13-2009 #3 milk123   Join Date: Feb 2009 Posts: 3 Exellent explaination but i'm looking for the algbratic equation. So for the sand and cement one could i say; 15a+1a = 6.6 16a = 6.6 a = 6.6/16 a=.4125 So therefore 15a = 6.1875L of gasoline 1a = .4125L of oil Does this one look correct? Last edited by milk123; 02-13-2009 at 07:40 PM..  02-13-2009 #4 milk123   Join Date: Feb 2009 Posts: 3 If i'm right about the oil and gas one, i'm lost on the other two.  05-29-2009 #5 shae marks   Join Date: May 2009 Posts: 1 word problem help? Hi everyone, i'm new here. Seems like a great educational site. Its been a while for me and i really need some help with the formula and explaination. The fuel for a two-cycle motorboat engine is a mixture of gasoline and oil in the ratio of 15 to 1. How many liters of each are in 6.6L of mixture? Fifty kilograms of a cement-sand mixture is 40% sand. How many kilograms of sand must be added for the resulting mixture to be 60% sand? A karat equals 1/24 part of gold in an alloy (for example, 9-karat gold is 9/24 gold). HOw many grams of 9-karat gold must be mixed with 18 karat gold to get 200g of 14-karat gold? Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Forum Rules
 Forum Jump User Control Panel Private Messages Subscriptions Who's Online Search Forums Forums Home Welcome     XP Math News     Off-Topic Discussion Mathematics     XP Math Games Worksheets     Homework Help     Problems Library     Math Challenges

All times are GMT -4. The time now is 10:12 PM.

 Contact Us - XP Math - Forums - Archive - Privacy Statement - Top XP Math