Annabeth, Grover, and Percy are shopping. Together, Annabeth and Grover have $43. If Grover and Percy combine their money, they have $55. Percy has $7 more than Grover. How much does each person have?

Grover has $24, Percy has $31 and Annabeth has $19.

Step-by-step explanation:

Create equations to represent the situation.

let a be Annabeth

let g be Grover

let p be Percy

a + g = 43 Together, Annabeth and Grover have $43

g + p = 55 If Grover and Percy combine their money, they have $55

p = g + 7 Percy has $7 more than Grover

See if any of the equations can be combined. For example, we know p is g+7.

Substitute p for g+7 in an equation that has the variable p.

g + p = 55

g + g + 7 = 55 Combine like terms (g)

2g + 7 = 55 Start isolating g. Subtract 7 from both sides

2g = 55 - 7

2g = 48 Divide both sides by 2

g = 48/2

g = 24 Money Grover has

Use the equation p = g + 7. Find "p" by substituting g for 24.

p = g + 7

p = 24 + 7 Add

p = 31 Money Percy has

Substitute g for 24 in the last equation, a + g = 43, to find a.

a + g = 43

a + 24 = 43 Subtract 24 from both sides

a = 43 - 24

a = 19 Money Annabeth has

Therefore Grover has $24, Percy has $31 and Annabeth has $19.