Question

Siti and Kate have 3049 beads altogether. Priya and Siti have 3647 beads in all Priya has 3 times as many beads as Kate. How many beads do the three girls have in total?
(This is a question for 4 graders)​

Answer 1

Answer:

The number of beads all three girls have in total is $3946$.

Step-by-step explanation:

Let the number of beads Siti have is $x$.

The number of beads Kate have is $y$.

The number of beads Priya have is $z$.

Given that,

$x+y=3049$   ...(1)

$x+z=3647$   ...(2)

$z=3y$              ...(3)

Substitute equation (3) in equation (2), we get

$x+3y=3647$  ...(4)

Now Subtracting equation (4) from equation (1), we get

(4)-(1)⇒

$x+3y-(x+y)=3647-3049$

$x+3y-x-y=598$

$2y=598$

$y=299$

Now substitute the value of $y$ in equation (1), we get

$x+299=3049$

$x=3049-299$

$x=2750$

Now substitute the value of $y$ in equation (3), we get

$z=3(299)$

$z=897$

Total number of beads all three girls have in total is

$x+y+z=2750+299+897$

$x+y+z=3946$.

Answer 2

Given,

Siti and Kate have $3049$ beads altogether.

Let Siti have beads be $x$

Let Kate have beads be $y$

From the given condition,

$x+y=3049$___(1)

Priya and Siti have $3647$ beads

Let Priya have beads be $z$

From the given condition,

$x+z=3647$___(2)

And priya has $3$ times as many beads as Kate

$z=3y$_____(3)

Substitute equation (3) in equation (2)

$x+3y=3647$___(4)

Now, subtract equation (4) to equation (1)

$x+3y-(x+y)=3647-3049$

$x+3y-x-y=3647-3049$

$2y=598$

$y=\frac{598}{2}$

$y=299$

Substitute $y=299$ in equation(1)

$x+299=3049$

$x= 3049-299$

$x=2750$

Substitute $y=299$ in equation (3)

$z= 3\times299$

$z= 897$

We have to find how many beads do the three girls have in total

$x+y+z=2750+299+897$

$= 3946$

Therefore, the answer is $3946$.