Original amount

Question

Jessica was preparing for her birthday party. She spent $3 less than 3/5 of her money on soft drink and $3 more than 3/4 of her remaining money on food. She still had $3 left. How much money did she start with?

Answer 1

she originally had $52.50. She spent $28.50 on soda, then another $21 on food, leaving $3 left

S= amount spent on soda

M= original amount

F= money spent on food

S= (3/5)M -3

F = 3 +(3/4)(M-S)

M-S-F = 3

3 linearly independent equations, 3 unknowns, 1 unique solution F=21, S= 28.5, M= 52.5

solve with substitution and elimination or matrix algebra

M-S=24

M-S-F = 3