Amy, Siti and Tina have a total of 730 story books. Tina has 50 more books than Amy. Amy has 70 books more than Siti. How many story books does Tina have?
S + (70+S) + (70 + S + 50) = 730
3 S + 190 = 730
3 S = 540
S = 180
(70 + S + 50) = 120+180 = 300
Let's start by assigning variables to the unknowns:
Let's say Amy has a number of books represented by "A".
Similarly, Siti's number of books is represented by "S".
And Tina's number of books is represented by "T".
We know that the total number of books they have is 730. So we can write an equation:
A + S + T = 730 (equation 1)
We also know that Tina has 50 more books than Amy. So we can write another equation:
T = A + 50 (equation 2)
Finally, we know that Amy has 70 books more than Siti. So we can write a third equation:
A = S + 70 (equation 3)
To find the number of books Tina has, we need to solve for variable "T".
We can solve this system of equations using substitution or elimination. Let's use substitution method.
Step 1: Substitute the value of A from equation 3 into equation 2:
T = (S + 70) + 50
T = S + 120
Step 2: Substitute the value of T from step 1 into equation 1:
(S + 70) + S + (S + 120) = 730
3S + 190 = 730
Step 3: Simplify the equation:
3S = 730 - 190
3S = 540
Step 4: Solve for S:
S = 540 / 3
S = 180
Step 5: Substitute the value of S back into equation 3 to find A:
A = 180 + 70
A = 250
Step 6: Substitute the value of S into equation 1 to find T:
250 + 180 + T = 730
T = 730 - 430
T = 300
Therefore, Tina has 300 story books.
To find out how many story books Tina has, we can use a system of equations. Let's assign variables to each person:
Let A be the number of books Amy has.
Let S be the number of books Siti has.
Let T be the number of books Tina has.
From the given information, we can deduce three equations:
1) A + S + T = 730 (The total number of story books they have is 730)
2) T = A + 50 (Tina has 50 more books than Amy)
3) A = S + 70 (Amy has 70 books more than Siti)
Now, we need to solve this system of equations. Let's substitute equation (3) into equation (2) to eliminate A:
T = (S + 70) + 50
T = S + 120
Now, we have a system of two equations:
1) A + S + T = 730
2) T = S + 120
We can substitute equation (2) into equation (1) to eliminate T:
(A + S + 120) + S = 730
A + 2S + 120 = 730
A + 2S = 610
Now we have two equations:
1) A + 2S = 610
2) T = S + 120
To solve this system of equations, we can use substitution or elimination method. Let's use the elimination method:
Multiply equation (2) by 2 to match the coefficient of S in equation (1):
2T = 2S + 240
Now, subtract equation (1) from this new equation:
2T - (A + 2S) = 2S + 240 - 610
2T - A - 2S = -370
Simplify:
2T - A - 2S = -370
Now, we have:
1) A + 2S = 610
2) 2T - A - 2S = -370
Add these two equations together:
(A + 2S) + (2T - A - 2S) = 610 - 370
2T = 240
T = 240/2
T = 120
Therefore, Tina has 120 story books.