Answer:
Ranjit has £6.50 altogether
Explanation:
To find out how much money Ranjit has altogether, we need to use algebraic equations. Let's assume that the value of the first coin is x, the second coin is y, the third coin is z, the fourth coin is a, the fifth coin is b and the sixth coin is c. Therefore, we can write:
x + y + z + a + b = £4.60 --- Equation 1
x + y + z + a + c = £2.70 --- Equation 2
To solve for the values of x, y, z, a, b and c, we need to use simultaneous equations. Subtracting Equation 2 from Equation 1, we get:
b - c = £1.90 --- Equation 3
Since we know that the value of each coin must be positive, we can assume that b > c. Therefore, we can rewrite Equation 3 as:
b = c + £1.90
Substituting this into Equation 1, we get:
x + y + z + a + (c + £1.90) = £4.60
x + y + z + a + c = £2.70
Subtracting these two equations, we get:
£1.90 = b - c = (c + £1.90) - c = £1.90
This means that b = £3.80 and c = £1.90.
Substituting these values back into Equations 1 and 2, we get:
x + y + z + a = £0.90 --- Equation 4
x + y + z + a = £0.80 --- Equation 5
Since Equations 4 and 5 are identical, this means that there are infinitely many solutions for x, y, z and a that satisfy the given conditions. Therefore, we cannot determine the exact amount of money that Ranjit has altogether.
However, we do know that the sum of all six coins must be equal to the sum of the five coins that Ranjit picked plus the value of the coin that he didn't pick. Therefore, we can write:
x + y + z + a + b + c = (sum of all six coins)
= (sum of five coins) + (value of sixth coin not picked)
= £4.60 + £1.90
= £6.50
Therefore, Ranjit has £6.50 altogether.