Year 8 algebra formula help!

[polarisng]

Could somebody please explain to me how to solve these problems? My son is in year 8 and he's having troubles with these advanced formulas (He could solve the easy ones). I need to learn how to do it so I can explain it to him.

For 1., I tried to subtract 57 to 45, 45 - 39, 39 - 15 to find the difference between the terms and the results were 12, 6, 24 respectively. I know that there's a relation between those 3 numbers but I just don't know how to put them together. Any help would greatly be appreciated. Thank you.

Write a formula expressing the second variable in terms of the first

1.
x 1 ---- 5 ---- 7 -----15
g 57 -- 45 --- 39 ----15

g = ?

-----------------------------------------

2.
x 5 ---- 6 ---- 12 ---- 15
y 80 ---76 --- 52 ---- 40

y = ?


-----------------------------------------

3.
z 15 ---- 10 ---- 7 ---- 5
y 0 ---- 30 ---- 48 -- 60

y = ?

 

[Deleted member 4993]

Could somebody please explain to me how to solve these problems? My son is in year 8 and he's having troubles with these advanced formulas (He could solve the easy ones). I need to learn how to do it so I can explain it to him.

For 1., I tried to subtract 57 to 45, 45 - 39, 39 - 15 to find the difference between the terms and the results were 12, 6, 24 respectively. I know that there's a relation between those 3 numbers but I just don't know how to put them together. Any help would greatly be appreciated. Thank you.

Write a formula expressing the second variable in terms of the first

1.
x 1 ---- 5 ---- 7 -----15
g 57 -- 45 --- 39 ----15
This is a linear relationship. For each increase of x by 1 - g decreases by 3
g = -3x + 60-----------------------------------------

2.
x 5 ---- 6 ---- 12 ---- 15
y 80 ---76 --- 52 ---- 40

y = ?

Similar linear relationship. For each increase in x - y decreases by 4
-----------------------------------------

3.
z 15 ---- 10 ---- 7 ---- 5
y 0 ---- 30 ---- 48 -- 60
Similar linear relationship. For each decrease in z - y decreases by 6
y = ?

.

 

[Mrspi]

Could somebody please explain to me how to solve these problems? My son is in year 8 and he's having troubles with these advanced formulas (He could solve the easy ones). I need to learn how to do it so I can explain it to him.

For 1., I tried to subtract 57 to 45, 45 - 39, 39 - 15 to find the difference between the terms and the results were 12, 6, 24 respectively. I know that there's a relation between those 3 numbers but I just don't know how to put them together. Any help would greatly be appreciated. Thank you.

Write a formula expressing the second variable in terms of the first

1.
x 1 ---- 5 ---- 7 -----15
g 57 -- 45 --- 39 ----15

g = ?

-----------------------------------------

2.
x 5 ---- 6 ---- 12 ---- 15
y 80 ---76 --- 52 ---- 40

y = ?


-----------------------------------------

3.
z 15 ---- 10 ---- 7 ---- 5
y 0 ---- 30 ---- 48 -- 60

y = ?

Without knowing what methods your son's class has been studying to approach this kind of problem, it is difficult for me to guess at what he's expected to do.

IF the class has been studying "linear relationships" and IF the information provided with this assignment indicates that the relationship in each problem is linear, there are indeed procedures which can be applied to come up with the "rule."

In the absence of information about the situation, I don't see any point in trying to go through the details of the process.

 

[polarisng]

Sorry, I'm not sure if he's studied linear relationships, but I think this is the "method" that he is supposed to follow, its the first page of this set of homework.






Subhotosh Khan, Can you please explain how you come to 3, 4 and 6?

Thank you

 

[tkhunny]

You need to behave sequentially.

x 1 ---- 5 ---- 7 -----15
g 57 -- 45 --- 39 ----15


x-values

5 - 1 = 4
7 - 5 = 2
15 - 7 = 8

These are the successive changes in the 'x' value - the independent variable.

g-values

45 - 57 = -12
39 - 45 = -6
15 - 39 = -24

You are trying to extablish the change in g, given the change in x. You cannot look at just g or just x. They must be considered together. This may suggest a ratio.

g / x

-12 / 4 = -3
-6 / 2 = -3
-24 / 8 = -3

 

[polarisng]

tkhunny, that makes a lot of sense!! THANK YOUUUU. I've just helped him with his homework =)

 

[pappus]

.

I don't want to pick at you but there is a small mistake in your calculations:

1.
x 1 ---- 5 ---- 7 -----15
g 57 -- 45 --- 39 ----15
This is a linear relationship. For each increase of x by 1 - g decreases by 3
g = -3x + 54
-----------------------------------------

The last line should read: g : -3x + 60

 

[Deleted member 4993]

Oh no ... that's good catch .... I am glad Denis did not see it before you did .... I would have been sent to corner by now.....