Respuesta :
Answer:
The total number of pounds of peaches is 1.5 pounds that Juan buys.
The total number of pounds of grapefruit is 1 pounds that Juan buys.
Step-by-step explanation:
Given : Juan buys peaches and grapefruit at the store. He writes the equations shown to model the relationship between the number of pounds of peaches, p, and the number of pounds of grapefruit, g, that he buys.
[tex]p + g = 2.5\\\\1.58p + 1.09g = 3.46[/tex]
To find : What is the total number of pounds of peaches and grapefruit that Juan buys?
Solution :
The equation,
[tex]p + g = 2.5[/tex]
[tex]p= 2.5-g[/tex] ....(1)
[tex]1.58p + 1.09g = 3.46[/tex] ....(2)
Substitute (1) in (2),
[tex]1.58(2.5-g)+ 1.09g = 3.46[/tex]
[tex]3.95-1.58g+ 1.09g = 3.46[/tex]
[tex]0.49g =0.49[/tex]
[tex]g =1[/tex]
Substitute in (1),
[tex]p= 2.5-1[/tex]
[tex]p=1.5[/tex]
The total number of pounds of peaches is 1.5 pounds that Juan buys.
The total number of pounds of grapefruit is 1 pounds that Juan buys.
By solving a system of equations we will see that Juan buys 1 pound of grapefruit and 1.5 pounds of peaches.
How to solve the system of equations?
Here we have the system:
p + g = 2.5
1.58p + 1.09g = 3.46
To solve this system, we first need to isolate one of the variables in one of the equations, I will isolate p on the first one.
p = 2.5 - g
Now we replace this on the other equation, we will get:
1.58*( 2.5 - g) + 1.09g = 3.46
Now we solve this for g.
3.95 - 1.58g + 1.09g = 3.46
3.95 - 0.49g = 3.46
3.95 - 3.46 = 0.49g
0.49 = 0.49g
0.49/0.49 = g = 1
Finally, we use:
p = 2.5 - g = 2.5 - 1 = 1.5
This means that Juan buys 1 pound of grapefruit and 1.5 pounds of peaches.
If you want to learn more about systems of equations, you can read:
https://brainly.com/question/13729904
