Joyce had some money. She bought a dress, a shirt and a watch. She spent 1/5 of her money on a shirt. The shirt cost $24 less than a dress. The watch cost $102. She was left with 1/4 of the amount of money she had at first. How much money did Joyce have at first?
Please help!!!!
amount of money she had at first ---- x
cost of shirt ------ x/5
"The shirt cost $24 less than a dress" ----> the dress cost 24 more than the shirt ------ x/5 + 24
shirt + dress + watch = (3/4)x,
(if 1/4 of her money is left, she must have spent 3/4 of it)
x/5 + x/5+24 + 102 = 3x/4
multiply each term by 20, to clear the fractions
4x + 4x + 480 + 2040 = 15x
take over
To find out how much money Joyce had at first, we can break down the information given step by step.
Let's denote the amount of money Joyce had at first as "x".
1) Joyce spent 1/5 of her money on a shirt:
So, the cost of the shirt is (1/5) * x.
2) The shirt cost $24 less than a dress:
Let's denote the cost of the dress as "d". Therefore, the cost of the shirt is "d - $24".
3) The watch cost $102:
So, the cost of the watch is $102.
4) Joyce was left with 1/4 of the amount of money she had at first:
Therefore, the amount of money Joyce was left with is (1/4) * x.
We can create an equation now:
x - [(1/5) * x + (d - $24) + $102] = (1/4) * x.
Simplifying the equation:
x - (1/5)x - (d - $24) - $102 = (1/4)x.
Multiplying all terms by 20 to eliminate fractions:
20x - 4x - 20 * (d - $24) - 20 * $102 = 5x.
Simplifying further:
16x - 20d + $480 - $2040 = 0.
Combining like terms:
16x - 20d - $1560 = 0.
We have one equation with two unknowns. Since we cannot solve for a specific value of "x" or "d", we cannot determine the exact amount of money Joyce had at first from the given information.