Question

Solve the following real-life problems.

Answer 1

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.