Can the values be added or subtracted? if one value needs to be converted to another, describe the conversion.
19.75 in² + 26.2 in³
the values cannot be added because one is measuring area and the other is measuring volume.
the values can be added without making a conversion of units because they both measure area.
the values can be added after making a conversion of units because they both measure area.
the values cannot be added because one is measuring area and the other is measuring mass.
the cost of one pair of sunglasses = $15
the cost of one pair of shirt = $18
let 'x' be the price of a pair of sunglasses and 'y' be the price of one shirt.
to form the equation
it is given that,
scarlet bought three pairs of sunglasses and two shirts for $81
we can write,
3x + 2y = 81 )
and paula bought one pair of sunglasses and five shirts for $105,
we can write,
x + 5y = 105 )
to find x and y
multiply eq(2) by 3 we get
3x + 15y = 315 )
eq(3) - eq(1) ⇒ 13y = 234
y = 234/13 = 18
eq(2) ⇒ x + 5y = 105
x + 5*18 = 105
x = 105 - 90 = 15
therefore, the cost of one pair of sunglasses= 15 and one shirt = 18
the wording leaves a little to be desired. what does that 32 actually mean?
i don't think it is asking us to add on the distance it has to travel to get a bounce of 32. we are starting with a bounce that is 32 high.
the second bounce is 9/10 of that height which turns out to be 28.8.
the third bounce is 9/10 of 28.8 which is 25.92, i think, and then it continues on.
so here are the givens
a = 32
r = 9/10
n = 25
sum = a(1 - r^n) / (1 - r)
sum = 32*(1 - (9/10)^25) / (1 - 9/10)
sum = 32*(1 - 0.07179) / ( 1 - 9/10)
sum = 32*(0.9282) / 0.1
sum = 29.7 / 0.1
sum = 297
but that number represents only the distance going up. you must also take the distance going down. you have to double this answer.
2*sum = 2 * 297
sum' = 594
the wording is a real snake. we don't really know if we need to include some height that was a start. if we do, the answer is 594 + k where k is a constant yet to be determined. usually k is part of the problem.
or do we take a = 32 as the first drop? we can't tell from the wording.