Mr. Logan purchased $390 in clothing (excluding sales tax). He bought 5 identical shirts, 3 identical pairs of pants and 2 identical pairs of shoes. Each pair of shoes cost twice the combined value of one shirt and a pair of pants. Each pair of pants cost $10 more than one shirt.

Question

Use let statements to express the cost of each item and relationship to each other.Write the equation to represent the situation.

Find the cost of 1 shirt, 1 pair of pants, 1 pair of shoes.

Help - I don't know how to use the let statements. Have already figured out the cost of each item (1 shirt is $20, 1 pants $30, 1 shoes $100)

Answer 1

In most cases it is advisable to define the smallest value, in this case the cost of a shirt

let each shirt cost x dollars
("Each pair of pants cost $10 more than one shirt. ---->)
let the cost of the pants be x+10

( "Each pair of shoes cost twice the combined value of one shirt and a pair of pants. ---->

let the cost of the shoes be 2(one shirt + one pants)
= 2(x + x+10)
= 4x + 20

5 shirts ----> 5x
3 pants ----> 3(x+10)
2 shoes ----> 2(4x+20)

5x + 3(x+10) + 2(4x+20) = 390
5x + 3x + 30 + 8x + 40 = 390
16x = 320
x = 20

so ...
1 shirt costs $20
1 pair of shoes costs $30
1 pair of pants costs $100

check:
5 shirts + 3 pants + 2 shoes
= 5(20) + 3(30) + 2(100)
= 390 YEAHHH

Answer 2

Thank you Reiny... you make it look so easy :)... thanks for the hint in starting with defining the smallest value.

Answer 3

You are welcome

another good idea is to underline or isolate key sentences, then "translate" them into "math"

Answer 4

when he left on vacation, the odometer in Carl's car read 32,654 miles. hen he returned from his trip it read 33,895. If he used 54.7 gallons of gas, how many miles per gallon did he get? Round to the nearest hundredth.