Algebra

A goldsmith has two gold alloys. The first alloy is 20% gold; the second alloy is 60% gold. How many grams of each should be mixed to produce 40 grams of an alloy that is 30% gold?
amount of 20% gold_____g
Amount of 60% gold_____g

1. 👍 0
2. 👎 1
3. 👁 360
1. grams 20 % = a
grams 60% = b

total gold = .2 a + .6 b
total mass = a + b = 40 so b = 40-a

so
.2 a + .6 b = .3 (40) = 12
.2 a + .6 (40-a) = 12
-.4 a + 24 = 12
.4 a = 12
a = 30
so
b = 10

1. 👍 0
2. 👎 0
2. It can be difficult to come up with formulas from word problems.

Your going to add some weight of the first alloy and some weight of the second allow to get 40 grams.
let x be the weight used from the first alloy and y the weight from the second.
so x+y=40

How much gold is in the 40 grams?

Well it's 30% gold, so
40*(.3)=12g of gold

likewise the amount of gold present from the first alloy would be 0.2x

the amount in the 60% sample is 0.6y

those two amounts add together to be the 12g of gold.

0.2x+0.6y=12

so two formulas, two variables.

if x+y=40 then
x=40-y

plug it in
0.2(40-y)+0.6(y)=12
8-0.2y+0.6y=12
0.4y=4
y=10

therefore x=30

check that it works to be safe
0.2(30)+0.6(10)=12
6+6=12
excellent.

hope this helps!

1. 👍 0
2. 👎 0
3. There is a rule for this class of problems of finding proportions of mixtures. Most of the time this can be done mentally, for example by chemists or nurses.

We have one ingredient A at 20%, and B at 60%. The required mixture is 30% (must be between those of A & B).

Take the difference between the ingredients, namely 60-20=40%.

The target percentage lies at 10% from A and 30% from B, or in the ratio 1:3

The proportions required for A and B will be 3:1, namely 30g of A and 10g of B.

1. 👍 0
2. 👎 0
4. Interesting approach Mathmate. Hadn't seen that before.

1. 👍 0
2. 👎 0

Similar Questions

1. Math

An alloy is composed of nickel, zinc, and copper in a ratio of 3:4:13. How many kilograms of each metal are needed to make 4 kg of this alloy?

2. Chemistry

Pure platinum is too soft to be used in jewelry because it scratches easily. To increase the hardness so that it can be used in jewelry, platinum is combined with other metals to form an alloy. To determine the amount of platinum

3. math

shanon needs 20g of 80% of gold to make a pendan. she has some 85% gold and some 70% gold, from broken jewelry and wants to know how much she should use. determine the quantity of each alloy that she should use.

4. Physical Science

Does this answer look correct? How many gold atoms are in a 1 kg gold bar? The chemical symbol of gold is Au. Consult The Periodic Table in Figure 11.9 on p. 216 in the textbook. Hint: Remember 1u=1.66x10-27kg. 1 mole= 6.022x1023,

1. algebra

A goldsmith has two gold alloys. The first alloy is 30% gold; the second alloy is 80% gold. How many grams of each should be mixed to produce 10 grams of an alloy that is 40% gold? amount of 30% gold ___ g amount of 80% gold ___ g

2. math

a metalworker has a metal alloy thay is 25% copper and another alloy that is 60% copper. how many kilograms of each alloy should the metalworker combine to create 90kg of a 53% coppet alloy

The "karat" is a dimensionless unit that is used to indicate the proportion of gold in a gold-containing alloy. An alloy that is one karat gold contains a weight of pure gold that is one part in twenty-four. What is the volume of

4. Physics, still don't get it!

The "karat" is a dimensionless unit that is used to indicate the proportion of gold in a gold-containing alloy. An alloy that is one karat gold contains a weight of pure gold that is one part in twenty-four. What is the volume of

1. Science

How many number of gold atom are present in 0.6 gm of 18 carat gold.The 24 carat gold is taken as 100% pure gold.(atomic mass of gold=197a.m.u)

2. Physics

A piece of gold-aluminium alloy weighs 49N when suspended from a spring balance and submerged in water it weighs 39.2N what is the weight of Gold in the alloy if the specific gravity of gold is 19.3 and aluminium is 2.5?

3. math

Anne and Nancy use a metal alloy that is 20.45% copper to make jewelry. How many ounces of a 12% alloy must be mixed with a 25% alloy to form 100 ounces of the desired alloy?

4. material science

A uniform compressive stress σz is applied to the surface of the metal alloy, and it may be assumed that there is no friction between the alloy and the die. This aluminum alloy has Young’s modulus E=70GPa and a Poisson’s