1. You have recently found a location for your bakery and have begun implementing the first phases of your business plan. Your budget consists of an $80,000 loan from your family and a $38,250 small business loan. These loans must be repaid in full within 10 years.
a. What integer would represent your total budget?
b. You will use 25% of your budget to rent business space and pay for utilities. Write an algebraic expression that indicates how much money will be spent on business space and utilities. Do not solve.
c. How much money will rent and utilities cost? Explain how you arrived at this answer.
d. Imagine an investor has increased your budget by $22,250. The investor does not need to be repaid. Rather, he becomes part owner of your business. Will the investor contribute enough money to meet the cost of rent and utilities? Support your answer and write an equation or inequality that illustrates your answer.
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.