Question

can someone explain and solve word problem? noah and kate are shopping for a new guitar strings in a music store. noah buys 2 packs of strings. kate buys 2 packs of strings and a music book. the book costs $16. their total cost is $72. how much is one pack of string? solve using multi-step equation

Answer 1

Okay, we know the price of a book = $16. We know that Noah buys 2 packs of strings, price unknown. We know that Kate buys 2 packs of strings and a book. Altogether, they spend $72. Let's write equations to show what know:

\[{Noah}_{spent} = 2*{Price}_{strings}\]\[{Kate}_{spent} = 2*{Price}_{strings}+1*{Price}_{book} = 2*{Price}_{strings}+1*$16 \]\[{Total}_{spent}={Noah}_{spent}+{Kate}_{spent} = $72\]
\[{Noah}_{spent}+{Kate}_{spent} = $72\]Replace with equations we worked out for how much each kid spent
\[(2*{Price}_{strings})+(2*{Price}_{strings}+1*$16) =$72\]Subtract $16 from each side to give\[2*{Price}_{strings}+2*{Price}_{strings}+1*$16 -$16 =$72-$16\]\[4*{Price}_{strings} =$56\]Divide both sides by 4\[{Price}_{strings} =$14\]

So a pack of strings costs $14. To check our work, 2*14+2*14+1*16 = 28+28+16=72