Answer:
a) The two numbers are x = 11 and y = 41
b) Leon gets $33, Kokyangwuti gets $16.5, Jill gets $38 and Isaac gets $6.5
c) Elizabet started with $106
Step-by-step explanation:
These problems can be solved by systems of equations
a)
I am going to say that the first number is x and the second number is y
The problem states that the sum of two numbers is 52. So x + y = 52.
The problem also states that one number is three less than quadruple the other number. So y = 4x - 3
We have the following system
1) x + y = 52
2) y = 4x - 3
Replacing 2) in 1)
x + 4x -3 = 52
5x = 55
x = 11
------
y = 4x - 3 = 4(11)-3 = 44-3 = 41
The two numbers are x = 11 and y = 41
b)
I am going to say that x is how much money Leon gets, y is how much Kokyangwuti, z is how much Jill gets and w is how much Isaac gets.
Martha divides $94 amongst her four friends. So x + y + z + w = 94
Leon gets twice as much money as Kokyangwuti. So x = 2y.
Jill gets five more dollars than Leon, so z = 5 + x
Isaac gets ten less dollars than Kokyangwuti, so w = y-10
We have the following system:
1) x + y + z + w = 94
2) x = 2y
3) z = 5 + x
4) w = y - 10
I am going to replace 2) in 3), so we have z = 5 + 2y
Now i am going to replace 2), 3) and 4) in 1), so:
2y + y + 5 + 2y + y - 10 = 94
6y -5 = 94
6y = 99
y = $16.5
From 2): x = 2y = 2*16.5 = $33
From 3) z = 5 + x = 5 + 33 = $38
From 4): w = y - 10 = $16.5-10 = $6.5
So, Leon gets $33, Kokyangwuti gets $16.5, Jill gets $38 and Isaac gets $6.5
c)
Elizabeth spent:
2 shirts for $22.99 each = $45.98
a drink for $2.02 = $2.02
2 books for $16 each = $32
In all, she spent 45.98 + 2.02 + 32 = $80
She has $26 left.
She started with $26 + $80 = $106.
