Ratio: Ratio that leads to Linear equation

A sum of money worth N103,025 consists of equal number of N1,000 notes, N500 notes, N50 notes, N20 notes, N10 notes and N5 notes respectively. Calculate how much of each note is contained in the sum.

Solution 

Given that

Total amount = N103,025

Currency notes = 1000, 500, 50, 20, 10 and 5

Number of notes involved = ?

Let no of notes = n

Then (1000*n) + (500*n) + (50*n) + (20*n) + (10*n) + (5*n) =  N103,025

1000n + 500n + 50n + 20n + 10n + 5n = N103,025

This forms an equation in n. simplifying further, we get

1585n = 103025

The coefficient of n is 1585

Divide both side by 1585 (coefficient of n) 

n = 103025 ÷ 1585     

n = 65

Thus, number of currency notes = 65 pieces in each denomination

Amount of each note is computed as follows

N1,000 notes = N1000 * 65

= N65,000

N500 notes   = N500 * 65

= N32,500

N50 notes   = N50 * 65

= N3,250

N20 notes   = N20 * 65

= N1,300

N10 notes   = N10 * 65

              = N650

N5 notes   = N5 * 65

             = N325

Check for correctness

To confirm, we sum up the values of all the denominations as follows

Denomination	Number	Amount
N1000	65	₦ 65,000.00
N500	65	₦ 32,500.00
N50	65	₦ 3,250.00
N20	65	₦ 1,300.00
N10	65	₦ 650.00
N5	65	₦ 325.00
		₦ 103,025.00