SOLUTION: Use two equations in two variables to solve the problem. According to the National Vital Statistics Reports, in 2004, the number of Americans who died from heart disease was abo

Question 785768: Use two equations in two variables to solve the problem.
According to the National Vital Statistics Reports, in 2004, the number of Americans who died from heart disease was about 6 times the number who died from accidents. If the total number of deaths from these two causes was 763,000, how many Americans died from each cause in 2004?

heart disease Americans
accidents Americans

Use two equations in two variables to solve the problem.
At a store, ice cream cones cost $0.90 and sundaes cost $1.65. One day a total of 155 cones and sundaes were sold and the receipts totalled $191.25. How many cones were sold? CONES
Found 2 solutions by mananth, josgarithmetic:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
x= Number of Americans died in accidents
y= Number of Americans who died with heart disease

1 x + 1 y = 763000 .............1
Total value
-6 x + 1 y = 0 .............2
Eliminate y
multiply (1)by -1
Multiply (2) by 1
-1 x -1 y = -763000
-6 x + 1 y = 0
Add the two equations
-7 x = -763000
/ -7
x = 109000
plug value of x in (1)
1 x + 1 y = 763000
109000 + y = 763000
y = 763000 -109000
y = 654000
y = 654000
x= 109000 Number of Americans died in accidents
y= 654000 Number of Americans who died with heart disease
------------------
x= Number of Cones
y= Number of Sundaes

1.00 x + 1.00 y = 155.00 .............1
Total value
0.90 x + 1.65 y = 191.25 .............2
Eliminate y
multiply (1)by -1.65
Multiply (2) by 1.00
-1.65 x -1.65 y = -255.75
0.90 x + 1.65 y = 191.25
Add the two equations
-0.75 x = -64.50
/ -0.75
x = 86
plug value of x in (1)
1.00 x + 1.00 y = 155.00
86.00 + y = 155.00
y = 155.00 -86.00
y = 69.00
y = 69
x= 86 Number of Cones
y= 69 Number of Sundaes
m.ananth@hotmail.ca

m.ananth@hotmail.ca

Answer by josgarithmetic(39615) (Show Source): You can put this solution on YOUR website!
National Vital Statistics, Deaths:
x = death from heart attack
y = accidents deaths

If total deaths 763000, then
The two equations form a system, and simple substitution for x will help you quickly find y.

Icecream & Cones:
c = how many cones
s = how many sundays (sundaes)
One day, . The given prices let us say .
The cost equation can be simplified very much: ,
.
Now multiply the count equation by 6 and subtract from the simplified cost equation.... or ignore this method and just use substitution if you want.

then

Using that value,
86 cones, 69 sundaes
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