Maths homework question year 4

[Serena1977]

So dd has this question for maths homework. I've worked it out by trial and error but I want to know if there is an easier way of doing it.

Star + heart = triangle
Star + triangle = cloud

Star is 2000 less than cloud
Heart is 1000 more than star

What numbers are cloud, triangle, heart and star?

Thanks

Can you do it using substitution
So insead if using triangle in the second line, use star +heart, so star +star + heart = triangle
Then you know that star +1000 =heart
So star + star + star +1000 = triangle etc

And then carry on in that vein

Star - 500
Heart - 1500
Triangle - 2000
Cloud - 2500

?

@kittybee

That's right but how did you do it other than trial and error?

@Findahouse21
But using that way doesnt bring the right answer, I'm confused

Star is 2000 less than cloud, which means than triangle is 2000.

Star plus heart must then equal 2000.

As countdowntonothing more eloquently said...

1. Star + heart = triangle
2. Star + triangle = cloud

1. Star + 2000 = cloud
2. Heart = star + 1000

Substitute 3 into 2:

Star + triangle = star + 2000

(- star from each side)
So triangle = 2000

Substitute 4 into 1

Star + star + 1000 = 2000
2 star = 1000
Star = 500

500 + heart = 2000
Heart = 1500

500 + 2000 = cloud
Cloud = 2500

Thank you all so much!

Put s and h in terms of c;

S = c-2000
H = s + 1000

So;
h = c - 2000 + 1000
H = c - 1000

substitute these into s +.t = c to find t
C -2000 + t = c
T = c - (c-2000)
T = 2000

Sub t= 2000 and s and h in terms of c into equation s + h = t
S + h = 2000
C -2000 + c - 1000 = 2000
2c - 3000 = 2000
2c = 5000
C = 2500

Sub c =2500 to find s
S = c-2000
S = 2500- 2000
S = 500

Sub s = 500 to find h
H =.s + 1000
H = 1500

So s = 500, h = 1500 t =.2000 c = 2500
S +h = t
S +t = c

I think! Probably is a more elegant way of doing this but I'm Typing on my phone and can't mostnofnwhat I've written.

I get star is 500, heart is 1500, triangle is 2000 & d is 2500.

I used excel though

With algebra the aim is to get rid of as many unknown letters as possible by expressing everything in terms of just one letter. So for example you know heart is 1000 more than star. So in the equation you replace heart with "star plus 1000". Eventually when you have expressed everything in terms of "star" you can work out what star is equal to.