Answer:
"Tanya bought 3 items that each cost the same amt"
"Let x represent the cost of one of Tanya's items"
So, Tanya bought 3 items, costing x+x+x = 3x
Note that (number of items)*(cost per item) = (number of items)*(cost/item) = cost, [item cancels out]
"Tony bought 4 items that each cost the same amt, but each was $2.25 less than the items Tanya bought."
The cost for Tony's items was: (x-2.25)+(x-2.25)+(x-2.25)+(x-2.25) = 4*(x-2.25)
"Tanya and Tony paid the same amt. of money"
This is an equation (the same amount means equals)
Tanya's cost = Tony's cost
a.) Write an equation. Let x represent the cost of one of Tanya's items
3x = 4(x-2.25)
Now, the math:
b.) Solve the equation. Show your work.
3x = 4(x-2.25)
3x = 4x - 9.00 [distributive principle; multiply]
-x = -9.00 [subtract 4x from both sides; option, could instead add 9.00, then subtract 3x from both sides, getting 9.00=x]
x = 9.00 [multiply both sides by (-1)]
[note: to "solve for x" means to find the value(s) of x that make the equation true,
so let's see if it is true --]
c.) Check your solution. Show your work.
Is 3x = 4(x-2.25), when x=9.00 ?
3(9.00) = 4(9.00-2.25) ?
27.00 = 36.00 - 9.00 ?
27.00 = 27.00 ?yes
d) State the solution in a complete sentence.
The problem started with: "Tanya bought 3 items that each cost the same amt. Tony bought 4 items that each cost the same amt, but each was $2.25 less than the items Tanya bought. Both Tanya and Tony paid the same amt. of money."
I would write: "Tanya bought 3 items, each costing $9.00. Tony bought 4 items, each costing $6.75. Tanya and Tony each paid $27.00."
Step-by-step explanation:
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