Kira, Alonzo, and Bob have a total of $130 in their wallets. Bob has 3 times what Alonzo has. Alonzo has 10$ less than Kira. How much do they have in their wallets?

Question

I would also like to be shown how to solve these types of problems, not just the answer.

Answer 1

Hi,

Kira = K, Alonzo = A, and Bob = B

Base of given information: B = 3A and A = K-10 and A + B + K = 130

now you know : B = 3A = 3 ( K-10) = 3K - 30

it is enough replace A & B in the made equation A + B + K = 130

K-10 + 3K-30 + k = 130 ----> 5k = 170 ----> K = 34

B = 3K - 30= 3( 34 ) -30 =72

A = K - 10 = 34 - 10 = 24

you can check you answer by adding A + B + K that will be 130,

I hope it is useful.

Minoo

Answer 2

First, we want to define some quantities so that we can translate this from a word problem to something we can see visually in equation form.

Let K = amount of money in $ that Kira has, A = amount of money in $ that Alonzo has, and B = amount of money in $ that Bob has.

We know that the total amount of money is $130, so we can say:

K + A + B = $130

We then are told that Bob has 3x as much money as Alonzo, so we can say:

B = 3A

Finally, we're told that Alonzo has $10 less than Kira, so we can say:

A = K – 10

The trick to questions like these is being able to find define one term in terms of the others, and then substitute these into our main equation to solve for that term, and then use it to find our other variables.

I see that I have A present in all 3 equations so far, so I am going to find B in terms of A, and K in terms of A, substitute these into my equation for total money, and solve for A.

A = K − 10, so K = A + 10

B = 3A

K + A + B = $130

By substitution,

(A + 10) + (A) + (3A) = 130

Combine like terms:

5A + 10 = 130

5A = 120

A = $24

Now, I can plug my value for A into my other equations to solve for B and K.

K = 24 + 10

K = $34

B = 3*24

B = $72

Therefore, Alonzo has $24 in his wallet, Kira has $34 in her wallet, and Bob has $72 in his wallet.

We can check our work by plugging our values for A, K, and B into our initial equation. We should find that the total values of Alonzo, Kira, and Bob's wallets equals $130.

K + A + B = $130

$34 + $24 + $72 = $130

Answer 3

These are systems of equations whereby the best way to solve these is to assign each person a variable and see if you can use the parts of the problem that relate them to each other in order to simplify the equations and make them easier to solve.

First let's say the amount of money Kira has is X, Alonzo is Y, and Bob is Z

We know together they have a total of $130, so write this as an equation:

1) X+Y+Z = 130

Now this is a single equation with 3 unknown variables (X,Y,Z). The general rule is that in order to solve for the variables you need at least as many equations as you have variables. So let's use other parts of the word problem to make more equations.

Bob has 3 times what Alonzo has will give us the equation:

2) Z = 3Y

Alonzo has $10 less than Kira will give us another equation:

3) Y = X - 10

So now we have 3 equations with our 3 unknowns (X,Y,Z) so we can use substitution in order to solve this system of equations. In general, the easiest way to do this is to take equations 2) and 3) and substitute them into equation 1) to get everything in terms of 1 variable.

Plugging in 2) into 1) for Z we get

X+Y+(3Y) = 130

Now rearrange equation 3) so we have X = Y+10 and plug into equation 1)

(Y+10)+Y+3Y = 130

Solve for Y:

5Y = 120

Y = 24

Now that we know what Y is, we can use that in equation 2) to get Z

Z = 3(24) = 72

And now you can use equation 3) to get X (you could also use equation 1 if you wanted)

24 = X - 10

X = 34

So the final values are X = 34 (Kira), Y = 24 (Alonzo), and Z = 72 (Bob)

Answer 4

Let K = Kira, A = Alonzo, and B = Ben based on how much money they have in their wallets.

K + A + B = 130

B = 3A

A = K - 10

These are the given equations we have so far.

1) Substitute K - 10 for A to get the following:

K + (K - 10) + 3(K - 10) = 130

2) Distribute the 3, combine like terms, divide both sides by 5 to get K by itself.

K + K - 10 + 3K - 30 = 130 → 5K - 40 = 130 → 5K = 170 → K = 34

3) Substitute 34 for K to find A.

A = 34 - 10 = 24

4) Substitute 24 for A to find B.

B = 3(24) = 72

Ben has $72, Alonzo has $24, and Kira has $34 in their wallets.

Answer 5

Hi, Lily!

so first a good thing to do when solving a word problem is to identify the variables.

Let K= Kira

Let A = Alonzo

Let B= Bob

Kira, Alonzo, and Bob have a total of 130.

So your first equation will be:

K+ A +B = 130

Bob has three times the amount that Alonzo has:

B= 3A

Alonzo has 3 less than Kira

A = K- 10 or K= A+ 10

Now you need to replace B with 3A and K with (A+3)

K+ A +B = 130

(A+ 10) + A + 3A = 130

Now that A is the only unknown we can now find how much money Alonzo has.

5A+ 10= 130

5A=‘120

A= 24

Now you can find B, bc B=3A

B=3(24)

B= 72

Finally you can find K bc, K=A+10

K= (24)+10

K=34

Answer: K=34 A= 24 and B=72

I hope this helps!