Question

An architect plans to buy 5 stone spheres and 3 stone cylinders. For the same​ amount, she can buy 2 stone spheres and 6 stone cylinders. If one stone cylinder costs ​$36.81​, how much does each stone sphere​ cost?

Answer 1

The cost of each stone sphere is $ 36.81

Solution:

Given that,

An architect plans to buy 5 stone spheres and 3 stone cylinders

For the same​ amount, she can buy 2 stone spheres and 6 stone cylinders

Let "x" be that same amount

Let "a" be the cost of each stone sphere

Cost of each stone cylinder = $ 36.81

Therefore,

x = 5 stone spheres and 3 stone cylinders

x = 5a + 3(36.81)

Similarly,

x = 2 stone spheres and 6 stone cylinders

x = 2a + 6(36.81)

Equate both,

$5a + 3(36.81) = 2a + 6(36.81)\\\\5a + 110.43 = 2a + 220.86\\\\5a - 2a = 220.86 - 110.43\\\\3a = 110.43\\\\a = 36.81$

Thus cost of each stone sphere is $ 36.81