a. The total budget can be represented by the sum of the family loan and the small business loan: 80,000 + 38,250 = $118,250.
b. An algebraic expression that represents the amount of money spent on business space and utilities would be 0.25 * total budget, where "total budget" is the sum of the family loan and the small business loan.
c. To calculate the cost of rent and utilities, we need to multiply the total budget by 25% (0.25) because 25% of the budget is allocated for these costs. So, the amount spent on rent and utilities would be 0.25 * 118,250 = $29,562.50.
d. The investor has increased the budget by $22,250. To determine if this is enough to cover the cost of rent and utilities, we need to compare the increased budget with the cost of rent and utilities. The equation would be: increased budget >= cost of rent and utilities.
Substituting the values, we have: 22,250 >= 29,562.50.
Since 22,250 is not greater than or equal to 29,562.50, the investor's contribution is not enough to meet the cost of rent and utilities.