At one store, a trophy costs $12.50 and engraving costs $0.40 per letter. At another store, the same trophy costs $14.75 and engraving costs $0.25 per letter.
How many letters must be engraved for the costs for this trophy at both stores to be the same?
Answer (3)
Answer : The number of letters engraved on each trophy must be 15.
Step-by-step explanation :
As we are given,
A trophy cost at one store = $ 12.50
Engraving cost per letter at one store = $ 0.40 × L
where, 'L' is number of letters.
A trophy cost at another store = $ 14.75
Engraving cost per letter at another store = $ 0.25 × L
Now we have to determine the number of letters must be engraved for the costs for this trophy at both stores to be the same.
12.50 + ( 0.40 × L) = 14.75 + ( 0.25 × L)
( 0.40 × L ) − ( 0.25 × L) = 14.75 − 12.50
0.15 × L = 2.25
L = ( 2.25 ) ÷ ( 0.15)
L = 15
Therefore, the number of letters engraved on each trophy must be 15.
When p is the number of letters being engraved: 12.5 + .4p = 14.75 + .25p -12.5 -12.5 .4p = 2.25 + .25p -.25p -.25p .15p = 2.25 /.15 /.15 p = 15 There would need to be 15 letters engraved for the cost of the trophies to be the same. Hope this helps!
The number of letters that must be engraved for the costs of the trophy at both stores to be the same is 15. This is found by setting the total costs from both stores equal and solving for the number of letters. After calculations, we determined that 15 letters will equalize the costs.
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