A shop sells 3 T-shirts and 2 shorts for $9.20. It also sells 4 T-shirts
and 5 shorts for $18.10. James spent $348 on a number of shorts and
T-shirts in the ratio of 3:5 respectively.
(a) Find the cost of one shorts.
(b) How many shorts did James buy?
3t+2s = 9.20
4t+5s = 18.10
solve for t and s as usual. Then use those values in
t*3x + s*5x = 348
solve for x
he bought 3x shorts
3t + 2s = 920
4t + 5s = 1810
1st times 4 ---> 12t + 8s = 3680
2nd times 3 ---> 12t + 15s = 5430
subtract them:
7s = 1750
s = 250
then subbing back, t = 140
A t-shirt costs $1.40, and shorts cost $2.50
James shorts and t-shiprts in ratio of 3:5 or 3x : 5x
3x(250) + 5x(140) = 34800
1450x = 34800
x = 24
so he bought 3(24) shorts and 5(24) t-hirts
= 72 shorts, 120 t-shirts
check:
72(250) + 120(140) = 34800 , looks good
To find the cost of one shorts and the number of shorts James bought, we can set up a system of equations based on the information given.
Let's assign variables to the cost of one shorts and T-shirt, respectively:
- Cost of one shorts = x
- Cost of one T-shirt = y
From the first statement, we know that the shop sells 3 T-shirts and 2 shorts for $9.20. This can be written as the equation:
3y + 2x = 9.20 (Equation 1)
From the second statement, we know that the shop sells 4 T-shirts and 5 shorts for $18.10. This can be written as the equation:
4y + 5x = 18.10 (Equation 2)
Now, we can solve this system of equations to find the values of x and y.
To solve this system of equations, we can use the method of substitution. We can solve Equation 1 for y and substitute it into Equation 2.
Solving Equation 1 for y, we get:
3y = 9.20 - 2x
y = (9.20 - 2x)/3 (Equation 3)
Substituting Equation 3 into Equation 2, we have:
4(9.20 - 2x)/3 + 5x = 18.10
Now, we can solve this equation for x.
Multiplying through by 3 to get rid of the fraction, we have:
4(9.20 - 2x) + 15x = 54.30
36.80 - 8x + 15x = 54.30
7x = 17.50
x = 17.50/7
x ≈ 2.50
So, the cost of one shorts is approximately $2.50.
Now, we can substitute the value of x back into Equation 3 to find y:
y = (9.20 - 2(2.50))/3
y = (9.20 - 5)/3
y = 4.20/3
y ≈ 1.40
So, the cost of one T-shirt is approximately $1.40.
Next, we can find the number of shorts James bought. We know that James spent $348 on a number of shorts and T-shirts in the ratio of 3:5 respectively.
Let's assume James bought 3k shorts and 5k T-shirts, where k is a constant.
The total amount James spent can be expressed as:
3k * (cost of one shorts) + 5k * (cost of one T-shirt) = $348
Substituting the values we found earlier:
3k * 2.50 + 5k * 1.40 = 348
7.50k + 7k = 348
14.50k = 348
k = 348/14.50
k ≈ 24
So, James bought approximately 3k shorts, which is approximately 3 * 24 = 72 shorts.
To summarize:
(a) The cost of one shorts is approximately $2.50.
(b) James bought approximately 72 shorts.