Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Get immediate and reliable answers to your questions from a community of experienced professionals on our platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
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!
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.
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.