SOLUTION: Hi. I am having complications solving two word problems involving inequalities. Please solve these and/or help me on these word problems. Thanks a lot! 1. Find the largest pair

Algebra ->  Inequalities -> SOLUTION: Hi. I am having complications solving two word problems involving inequalities. Please solve these and/or help me on these word problems. Thanks a lot! 1. Find the largest pair      Log On


   

Question 432674: Hi. I am having complications solving two word problems involving inequalities. Please solve these and/or help me on these word problems. Thanks a lot!
1. Find the largest pair of consecutive even integers whose sum is less than 85.
2. Eve's grades on three tests were 78, 93, and 63. What is the lowest grade she can get on the next test to have an average higher than 80?
Thanks again!
Megan, 13 year old Algebra student

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1. Find the largest pair of consecutive even integers whose sum is less than 85.
:
Let the 2 consecutive even integers = x, (x+2)
;
the equation for the given statement:
x + (x+2) < 85
Combine like terms:
2x + 2 < 85
subtract 2 from both sides:
2x < 85 - 2
2x < 83
Divide both sides by 2
x < 83%2F2
x < 41.5
therefore
40, 42, are the largest even consecutive integer
:
Check this
40+42 = 82
:
:
2. Eve's grades on three tests were 78, 93, and 63.
What is the lowest grade she can get on the next test to have an average higher than 80?
:
Let x = her grade on the 4th test
:
The equation
%28x%2B78%2B93%2B63%29%2F4 > 80
%28x%2B234%29%2F4 > 80
Multiply both sides by 4
x + 234 > 4(80)
x + 234 > 320
Subtract 234 from both sides
x > 320 - 234
x > 86
She will need at least an 87 to have an average greater than 80
;
:
Check this:
%2887%2B78%2B93%2B63%29%2F4 =
321%2F4 = 80.25, just greater than an 80 average