Afoundry has been commissioned to make souvenir coins. the coins are to be made from an alloy that is 40% silver. the foundry has on hand two alloys, one with 50% silver content and one with a 25% silver content. how many kilograms of each alloy should be used to make 10 kilograms of the 40% silver alloy? 50% alloy = ? kg 25% alloy = ? kg

6 kilograms of 50% silver alloy and 4 kilograms of 25% silver alloy should be used.

Explanation

Suppose, the weight of the alloy with 50% silver content is kilograms.

As, the weight of the mixed alloy should be 10 kilograms, so the weight of the alloy with 25% silver content will be: kilograms

The percentage of silver content in the mixed alloy is 40%. So the equation will be .......

So, the amount of 50% silver alloy is 6 kilograms and the amount of 25% silver alloy is (10-6)= 4 kilograms.

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt

answer: 1+1

step-by-step explanation: 1+1 is at least 2