Solve the following real-life problems.
a. the sum of two numbers is 52. one number is three less than quadruple the other number. what are the two numbers? 

b. martha divides $94 amongst her four friends. leon gets twice as much money as kokyangwuti. jill gets five more dollars than leon. isaac gets ten less dollars than kokyangwuti. how much money does each friend get? 

c. elizabeth has $26 left after shopping at the mall. she bought 2 shirts for $22.99 each, a drink for $2.02, and 2 books for $16 each. how much money did she start with? 


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.