coolawesomeryan
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Question for Math! I have a 200-point math test coming up, and I don't get the concept of this question, but if somebody is willing to help me out on this question, well, 50 points + brainliest! PLEASE help!
Anthony is five years older than Chase. Trinity is twice as old as Anthony, The sum of their ages is 59. How old is each person?
Work please, and at the end, there should be three answers.
Thank you so much!!!!!! :D

Sagot :

Answer:

Anthony is 16, Chase is 11, Trinity is 32

Step-by-step explanation:

This is going to be very lengthy!

[tex]x= Anthony, y= Chase, z= Trinity[/tex]

---

1. [tex]x=y+5[/tex]

2. [tex]z=2x[/tex]

3. [tex]x+y+z=59[/tex]

Anthony is 5 years older than Chase, so Chase's Age + 5 is equal to Anthony's age

Trinity is twice as old as Anthony, so Trinity is 2*Anthony's age

Their sum is 59, so all of their ages added together should equal 59

Since this is a system of three equations, you have to shrink it down to 2 equations with only 2 variables. To do that, I'll be using elimination between 2 equations 1 at a time. Matrices would be faster and cleaner, but I'll do it algebraically!

1 & 2:

[tex]x-y=5\\-2x+z=0\\---\\2x-2y=10\\-2x+z=0\\---\\-2y+z=10[/tex]

This is going to be one of my new equations since it now only has 2 variables, which we want! NOTE: Whicever variable you eliminate from the first equation, you HAVE TO eliminate that some one from the reminaing two equations.

2 & 3:  

[tex]-2x+z=0\\x+y+z=59\\---\\-2x+z=0\\2x+2y+2z=118\\---\\2y+3z=118[/tex]

Notice how I have 2 equations, both with the same variables (y & z). I can use those two now to create a system of 2 equations!

[tex]-2y+z=10\\2y+3z=118\\---\\4z=128\\z=32\\---\\-2y+32=10\\-2y=-22\\y=11\\---\\32=2x\\x=16[/tex]

Anthony is 5 years older than Chase: [tex]11+5=16[/tex] is true

Trinity is twice as old as Anthony: [tex]16*2=32[/tex] is true

Their sum is 59: [tex]16+11+32=59[/tex] is true

Hope that helps!

semsee45

Answer:

Anthony is 16 years old.

Chase is 11 years old

Trinity is 32 years old.

Step-by-step explanation:

Define the variables:

  • Let a = Anthony's age
  • Let c = Chase's age
  • Let t = Trinity's age

Given information:

  • Anthony is five years older than Chase.
  • Trinity is twice as old as Anthony.
  • The sum of their ages is 59.

Create 3 equations from the given information and defined variables:

[tex]\textsf{Equation 1}: \quad a = c + 5[/tex]

[tex]\textsf{Equation 2}: \quad t = 2a[/tex]

[tex]\textsf{Equation 3}: \quad a + c + t = 59[/tex]

Rearrange Equation 1 to isolate c:

[tex]\implies c=a-5[/tex]

Substitute this and Equation 2 into Equation 3 and solve for a:

[tex]\implies a+c+t=59[/tex]

[tex]\implies a+a-5+2a=59[/tex]

[tex]\implies 4a-5=59[/tex]

[tex]\implies 4a-5+5=59+5[/tex]

[tex]\implies 4a=64[/tex]

[tex]\implies \dfrac{4a}{4}=\dfrac{64}{4}[/tex]

[tex]\implies a=16[/tex]

Substitute the found value of a into Equation 1 and solve for c:

[tex]\implies a=c+5[/tex]

[tex]\implies 16=c+5[/tex]

[tex]\implies 16-5=c+5-5[/tex]

[tex]\implies c=11[/tex]

Substitute the found value of a into Equation 2 and solve for t:

[tex]\implies t=2a[/tex]

[tex]\implies t=2(16)[/tex]

[tex]\implies t=32[/tex]

Therefore:

  • Anthony is 16 years old.
  • Chase is 11 years old
  • Trinity is 32 years old.
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