Suzie, Jackie and Tom shares $353.

Question

Suzie, Jackie and Tom share $353. Jackie has $22 more than Suzie, and Tom has three times as much money as Jackie. How much money do Suzie and Tom have altogether?

 

Please tell me the final answer.

Answer 1

Hi Reyna, let S represent Suzie, J represent Jackie, and T represent Tom. 

 

Then:

 

J = S + 22

 

T = 3 * J = 3 * (S + 22)

 

Equation:

 

S + J + T = 353

 

Substitute for J and T:

 

S + (S + 22) + 3 * (S + 22) = 353

 

Remove parenthesis and combine:

 

5S + 88 = 353

 

Subtract 88 from both sides:

 

5S = 265

 

Divide both sides by 5:

 

S = 53

 

J = S + 22, or 53 + 22 = 75

 

T = 3 * J, or 3 * 75 = 225

 

Check:

 

S + J + T = 353

 

53 + 75 + 225 = 353

 

353 = 353

 

Values check.

 

Therefore:

 

Suzie has: $53.

 

Jackie has: S + 22, $53 + $22 = $75

 

Tom has: 3 * J, 3 * $75 = $225.

 

Suzie + Tom = $53 + $225 = $278

 

Questions?

Answer 2

It helps to define your variables first.

 

Let s = Suzie's money

Let j = Jackie's money

Let t = Tom's money

 

Now use your variables to write the information given in mathematical terms.

 

"Suzies, Jackie, and Tom share $353." => s + j + t = 353

"Jackie has $22 more than Suzie..." => j = s + 22

"...Tom has three times as much money as Jackie." => t = 3j

 

It looks like it would be easy to define all variables in terms of j, then substitute into the first equation to solve for j. The other variables can be found as a result of j.

 

j = s + 22, so:

s = j - 22

t = 3j

 

Sub in to the top equation:

s + j + t = 353

j - 22 + j + 3j = 353  Simplify.

5 j - 22 = 353            Add 22 to both sides to get the j term on its own.

5j = 375                   Divide both sides by 5 to get j alone.

j = 75

 

If j = 75, s = 75 - 22 = 53, and t = 3 (75) = 225. Check: Is 225 + 53 + 75 equal to 353? Yes!