Respuesta :
Answer:
[tex]let \: jerry = x \\ let \: perry = y \\ jerry \: is \: twice \\ 2x + y = 0 \: \: \: equation1 \\ the \: combine \: age \\ x + y = 112 \: \: \: \: equation \: 2 \\ substitution \: method \\ make \: x \: the \: subject \: of \: formula \: from \: equation \: 2 \\ x = 112 - y \\ substitute \: x = 112 - y \: into \: equation \: 1 \\ 2x + y = 0 \\ 2(112 - y) + y = 0 \\ 224 - 2y + y = 0 \\ 224 - y = 0 \\ collect \: like \: terms \\ - y = - 224 \\ \frac{ - 2}{ - } = \frac{ - 224}{ - } \\ y = 224 \\ substitute \: y = 224 \: into \: equation \: 3 \\ x = 112 - y \\ x = 112 - 224 \\ x = - 112[/tex]
x = 224, y = -112
Twice as old means double of what we're referring to. The age of Jerry and Perry are: Jerry is 64 years old and Perry is 48 years old.
How to form mathematical expression from the given description?
You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
For the given case, the ages of Jerry and Perry are unknown. Let them be denoted by variables as:
- Age of Jerry currently = [tex]J_{new}[/tex]
- Age of Perry currently = [tex]P_{new}[/tex]
And let the in the past about which the question is talking about , we had:
- Age of Jerry in that past = [tex]J_{old}[/tex]
- Age of Perry in that past= [tex]P_{old}[/tex]
It is given that Jerry is twice as old as Perry was when Jerry was as old as Perry is now.
"Jerry was as old as Perry is now" means [tex]J_{old}[/tex] = [tex]P_{new}[/tex]
Also, know that:
[tex]J_{new} - J_{old} = P_{new} - P_{old}[/tex] since same time passed for both of them from considered past till now.
Thus,
[tex]J_{new} - J_{old} = P_{new} - P_{old}\\\\J_{new} = J_{old} + P_{new} - P_{old} = 2P_{new} - P_{old}[/tex] (first equation)
"Jerry is twice as old as Perry was" for that past, we have:
[tex]J_{new} = 2 \times P_{old}[/tex] (second equation)
From first and second equation, we get:
[tex]2P_{old} = 2P_{new } - P_{old}\\\\3P_{old} = 2P_{new}\\\\P_{old} = \dfrac{2P_{new}}{3}[/tex]
Thus, from this result and second equation, we get:
[tex]J_{new} = 2P_{old} = 2\times { \dfrac{2P_{new}}{3}} = \dfrac{4P_{new}}{3}[/tex]
Since it is given that:
[tex]J_{new} + P_{new} = 112[/tex]
Thus, putting J(new)'s value in this equation, we get:
[tex]J_{new} + P_{new} = 112\\\\\dfrac{4P_{new}}{3} + P_{new} = 112\\P_{new} = \dfrac{3 \times 112}{7} = 48[/tex]
Thus, we get the value for the Jerry now as:
[tex]J_{new} = \dfrac{4P_{new}}{3} = \dfrac{4 \tmies 48 }{3} = 64[/tex]
Thus, the age of Jerry and Perry are: Jerry is 64 years old and Perry is 48 years old.
Learn more about solving equations here:
https://brainly.com/question/498084
