So we have
h=hits
m=miss
h+m=10
gain 5 for every hit and lose 3 for every miss
so 5 times number of hit=points from hit
-3 times number of miss=points deducted from miss
add
5h-3m=18
so we have the equations
h+m=10
5h-3m=18
multiply first equation by 3
3h+3m=30
add to first equatio
3h+3m=30
<u>5h-3m=18 +</u>
8h+0m=48
8h=48
divide by 8
h=6
subsitute
h+m=10
6+m=10
subtract 6
m=4
6 hits
4 miss
<u />
The oldest cousin should be 10. If their ages are consecutive even whole numbers, then the younger cousins should be 2 & 4. 2+4=6+10=16
Simplifying
2x2 + 6x + 4 = 24
Reorder the terms:
4 + 6x + 2x2 = 24
Solving
4 + 6x + 2x2 = 24
Solving for variable 'x'.
Reorder the terms:
4 + -24 + 6x + 2x2 = 24 + -24
Combine like terms: 4 + -24 = -20
-20 + 6x + 2x2 = 24 + -24
Combine like terms: 24 + -24 = 0
-20 + 6x + 2x2 = 0
Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 3x + x2) = 0
Factor a trinomial.
2((-5 + -1x)(2 + -1x)) = 0
Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:
Simplifying
-5 + -1x = 0
Solving
-5 + -1x = 0
Move all terms containing x to the left, all other terms to the right.
Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5
Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5
Combine like terms: 0 + 5 = 5
-1x = 5
Divide each side by '-1'.
x = -5
Simplifying
x = -5
