Explain how to solve this, step by step?Together, a chair, a table, and a lamp cost $562. The chair costs 4 times as much as the lamp, and the table costs $23 less than the chair. Calculate the cost of the chair, the table, and the lamp.
Accepted Solution
A:
Answer:The cost of chair is [tex]\$260[/tex]The cost of a lamp is [tex]\$65[/tex]The cost of a table is [tex]\$237[/tex]Step-by-step explanation:Letx----> the cost of chairy----> the cost of lampz----> the cost of tablewe know that[tex]x+y+z=562[/tex] ----> equation A[tex]x=4y[/tex] -----> [tex]y=x/4[/tex] -----> equation B[tex]z=x-23[/tex] ------> equation Csubstitute equation C and equation B in equation A and solve for x[tex]x+(x/4)+(x-23)=562[/tex][tex](9/4)x=562+23[/tex][tex](9/4)x=585[/tex][tex]x=585*4/9=\$260[/tex]Find the value of y[tex]y=260/4=\$65[/tex]Find the value of z[tex]z=260-23=\$237[/tex] thereforeThe cost of chair is [tex]\$260[/tex]The cost of a lamp is [tex]\$65[/tex]The cost of a table is [tex]\$237[/tex]