8. A goldsmith has 130 grams of a gold alloy (a mixture of gold and one or more other metals) containing 85% pure gold. How much pure gold must be added to this alloy to obtain an alloy that is 90% pure gold?
The amount of pure gold that should be added is
(Type an integer or a decimal.)
grams.

65 grams

Step-by-step explanation:

If 130 grams of a gold alloy (a mixture of gold and one or more other metals) containing 85% pure gold, that means the percentage of other metals will be;

100 - 85 = 15 %

You should first calculate the amount of gold that makes up this percentage.

That is, 85% of 130 grams.

85/100 × 130 = 110.5

Then, let X be what will be added to the above value to make 90%. So,

(110.5 + X) / ( 130 + X ) × 100 = 90

Divide both sides by 100

(110.5 + X) / ( 130 + X ) = 90/100

(110.5 + X) / ( 130 + X ) = 0.9

Cross multiply and open the bracket

110.5 + X = 117 + 0.9X

Collect the like terms

X - 0.9X = 117 - 110.5

0.1X = 6.5

Divide both sides by 0.1

X = 6.5/0.1

X = 65 grams

Therefore, the amount of pure gold that should be added is 65 grams

hi,

you half the rectangle that you ae asking about so then you would see the scale factor of 1/2 the one u have selected, the one on top is half.

hope this !