Question

A country will produce 3000 missiles this year. Each of the short-range missiles cost $200000 to produce. Each of the medium-range missiles cost $300,000 to produce. The ratio of the number of short-range to medium range to long-range missiles the country plans to produce this year is 3:3:4. The countries plans to use 870 million dollars to produce these missiles. How much does it cost to produce a long-range missile?

Answer 1

$350,000

Explanation:

Let's define:

• s: amount of short-range missiles produced

• m: amount of medium-range missiles produced

• l: amount of long-range missiles produced

From the total production and the ratios we can write the following equations:

s + m + l = 3000

s/m = 3/3 = 1 = m/s

s/l = 3/4 or l/s = 4/3

Dividing the first equation by s, we get:

s/s + m/s + l/s = 3000/s

1 + 1 + 4/3 = 3000/s

10/3 = 3000/s

s = 3000*3/10 = 900

m = 900

l = 4/3*900 = 1200

From the money that the countries plans to use and each missile cost, we can write the following equation:

200,000*s + 300,000*m + cost*l = 870,000,000

Replacing with previous result:

200,000*900 + 300,000*900 + cost*1200 = 870,000,000

cost = (870,000,000 - 200,000*900 - 300,000*900)/1200 = 350,000