1.A shirt cost $15 more than a pair of shorts. Terrell paid $101 for 3 shirts and 5 pairs of shorts. How much did each shirt cost?
2. A watch cost $ 48 more than a clock. The clock of the clock is 4/7 the cost of the watch. Find the total cost of the 2 items.
3 s + 5( s-15) = 101
8 s - 75 = 101
8 s = 176
s = 22
c = 4 w/7
w = c + 48
w = 4 w / 7 + 48
7 w = 4 w + 336
3 w = 336
w = 112
c = 4 * 112 / 7 = 64
Let's break down each problem step by step.
1. To find the cost of each shirt, we need to set up a system of equations based on the given information.
Let's say the cost of a pair of shorts is "x".
According to the problem, a shirt costs $15 more than a pair of shorts, so the cost of a shirt is "x + $15".
Terrell paid $101 for 3 shirts and 5 pairs of shorts. We can write this as an equation:
3(x + $15) + 5x = $101
Simplifying the equation:
3x + $45 + 5x = $101
8x + $45 = $101
8x = $101 - $45
8x = $56
To find the value of "x", we divide both sides of the equation by 8:
x = $56 / 8
x = $7
Now that we know the cost of a pair of shorts is $7, we can find the cost of a shirt by adding $15 to it:
Cost of a shirt = $7 + $15 = $22
Therefore, each shirt cost $22.
2. To find the total cost of the watch and the clock, we need to set up an equation based on the given information.
Let's say the cost of the clock is "x".
According to the problem, the cost of the watch is $48 more than the clock, so the cost of the watch is "x + $48".
The clock is 4/7 the cost of the watch, which means:
x = (4/7) * (x + $48)
To solve this equation, we can get rid of the fraction by multiplying both sides by 7:
7x = 4(x + $48)
Expanding the equation:
7x = 4x + 4($48)
7x = 4x + $192
Subtracting 4x from both sides:
7x - 4x = $192
3x = $192
To find the value of "x", we divide both sides of the equation by 3:
x = $192 / 3
x = $64
Now that we know the cost of the clock is $64, we can find the cost of the watch by adding $48 to it:
Cost of the watch = $64 + $48 = $112
The total cost of the clock and the watch is obtained by summing their costs:
Total cost = $64 + $112 = $176
Therefore, the total cost of the two items is $176.