Question

Luke has $21 more than rachel and $48 more than daniel. altogether they have $168. how much does luke have?

Answer 1

Let Luke be represented as L , rachel be represented as R and daniel be represented as D

As per the statement: Luke has $21 more than rachel and $48 more than daniel

⇒
`L = 21 +R` and L = 48+D

equate these two we get;

21 + R = 48 + D

we can write this as;

R = 48+D -21

R = 27 +D ......[1]

Also, it is given that altogether they have $168.

⇒
`L+R+D = 168` .....[2]

Substitute the value of L=21+R in equation [2] we have;

`21+R+R+D= 168`

Combine like terms;

`21+2R+D= 168`

Subtract 21 from both sides we get;

2R+D= 147 ......[3]

Substitute the value of equation [1] in [3] we get;

2(27+D)+D = 147

Using distributive property;
`a\cdot (b+c) = a\cdot b +a\cdot c`

54 + 2D +D = 147

Combine like terms;

54 +3D =147

Subtract 54 from both sides we get;

3D = 93

Divide both sides by 3 we get;

D = $31

Now, substitute this value of D in L = 48+D we have;

L = 48 + 31 = $79

Therefore, $79 does Luke have.