Question 1205706: The sum of two numbers is 13. One number is 25 less than the other. Find the numbers.
The smaller number is:
The larger number is:
The perimeter of a rectangle is 124. The length is 4 less than
5 times the width. Find the width and length.
Width:
Length:
The measure of one of the small angles of a right triangle is 29 less than 6 times the measure of the other small angle. Find the measure of both angles.
Smallest angle:
Other non-right angle:
Jerome currently sells stoves for Gabriela's Stove Store at a salary of $16,000 plus a $10 commission for each stove he sells. Logan's Stove Store offers him a position with a salary of $13,000 plus a commission of $25 for each stove he sells. How many stoves would he need to sell for the options to be equal?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! The sum of two numbers is 13. One number is 25 less than the other. Find the numbers.
The smaller number is:
The larger number is:
x is the larger number
y is the smaller number
x + y = 13
y = x - 25
replace y with x - 25 to get x + x - 25 = 13
combine like terms and add 25 to both sides of the equation to get 2x = 38
solve for x to get x = 19
y = x - 25 means y = -6
x = 19 and y = -6 is your answer.
-6 + 19 = 13.
answer is confirmed to be correct.
The perimeter of a rectangle is 124. The length is 4 less than
5 times the width. Find the width and length.
Width:
Length:
p = 2l + 2w
p = 124 so the formula becomes 124 = 2l + 2w
l = 5w - 4 so the formula becomes 124 = 2 * (5w-4) + 2w
simplify and combine like terms to get 124 = 12w - 8
add 8 to both sides to get 132 = 12w
solve for w to get w = 132 / 12 = 11
l = 4 less than 5w gets you l = 51
dimensions are l = 51 and w = 11
2l + 2w gets you 102 + 22 = 124
this confirms the dimensions are correct.
your solution is length = 51 and width = 11.
The measure of one of the small angles of a right triangle is 29 less than 6 times the measure of the other small angle. Find the measure of both angles.
Smallest angle:
Other non-right angle:
right triangle has one 90 degree angle and 2 angles that are each less than 90 degrees.
one of the smaller angles is x.
the other is y.
sum of the angles of the triangle is 180 degrees.
subtract the 90 degree angle to get the sum of the smaller angles is 90.
formula becomes x + y = 90
let x = 6y - 29
replace x with that to get 6y - 29 + y = 90
combine like terms and add 29 to both sides to get 7y = 119
solve for y to get y = 119/7 = 17
x = 6y - 29 makes x = 73
you have x = 73 and y = 17
73 + 17 = 90 and 6 * 17 - 29 = 73 confirms the values of the angles are correct.
x = 73 and y = 17 is your answer.
Jerome currently sells stoves for Gabriela's Stove Store at a salary of $16,000 plus a $10 commission for each stove he sells. Logan's Stove Store offers him a position with a salary of $13,000 plus a commission of $25 for each stove he sells. How many stoves would he need to sell for the options to be equal?
16000 + 10x = 13000 + 25x is the break even point.
subtract 13000 from both sides and subtrasct 10x from both sides to get 3000 = 15x
solve for x to get x = 3000 / 25 = 200
the options are equal when he sells 200 stoves.
at the break even point:
16000 + 10 * 200 = 18000
13000 + 25 * 200 = 18000
he will have made 18000 with either option.
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