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Question

For every 5 dollars that a not-for-profit
foundation transferred to a relief fund,
the Government donated another 4 dollars towards the same cause.
After 10 months of fund raising, the foundation had a total of $22,814 including the Government's contribution.
Calculate the amount donated by the Government.

Answer 1

If we set X₁ =  public donations and X₂ = government match we can set the following relation:

X₂ = 4/5X₁ since the government donated $4 for every $5 of public donations.

The equation for total donations is as follows:

X₁ + X₂ = $22,814 since the total amount contributed is simply the sum of the government and public donations.

Substitute X₂ from the first relation in this equation and you have:

X₁ + 4/5X₁ = $22,814

Solve this for X₁:

1.8X₁ = $22,814

X₁ = $12,674.44

Then use this value to solve the first relation for X2:

X₂ = 4/5X₁

X₂ = 0.8($12,764.44)

X₂ = $10,139.56