Question 1134285: Giovanni wants to buy shirts that cost $19.40 each and sweaters that cost $24.80 each. An 8% sales tax will be applied to the entire purchase. If Giovanni buys 2 shirts, which equation relates the number of sweaters purchased, p, and the total cost in dollars, y?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! p = number of sweaters purchased.
shirts cost 19.40 each.
sweaters cost 24.80 each.
8% sales tax is applied to the total purchase.
giovanni buys 2 shirts and p sweaters.
his total purchase price would be 2 * 19.40 + p * 24.80.
add 8% to this and the total cost is 1.08 * (2 * 19.40 + p * 24.80)
simplify to get total cost is 41.904 + 26.784 * p
let y = total cost in dollars and your equation becomes y = 41.904 + 26.784 * p
i think that's what you're looking for.
the formula is valid regardless of the number of sweaters purchased.
for example, if the number of sweaters purchased is 10, then the formula becomes y = 41.904 + 26.784 * 10 which becomes y = 41.904 + 267.84 which becomes y = 309.744.
your solution is that the equation that relates the total cost to the number of sweaters purchased is y = 41.904 + 26.785 * p.
if youo don't add the tax until the end, then the equation can also be shown as:
y = 2 * 19.40 + p * 24.80 + .08 * (2 * 19.40 + p * 24.80)
this formula can also be written as y = 38.8 + 24.8 * p + .08 * (38.8 + 24.8 * p)
this formula can also be written as y = 1.08 * (38.8 + 24.8 * p)
this formula can also be written as y = 41.904 + 26.784 * p which is the formula that was originally created up above.
all these formulas give you the same answer.
they're just each written a little differently from each other.
since they all give the same answer, they're equivalent.
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