Loyola heights has 3000 phones of which 3/5 are dial phones. If 2/3 of these dial phones are replaced by digital phones and 400 additional phones are installed, what fraction of the phones are digital now?
digital=replacements+new
=3000*3/5*2/3 + 400
total phones: 3000+400
percentdigital= digital/total x 100
1600/3400=.4705 * 100 =47
key said 2/5.
To find the fraction of the phones that are digital now, we need to calculate the number of digital phones and divide it by the total number of phones.
Let's go step by step:
1. Calculate the number of dial phones:
If 3/5 of the 3000 phones are dial phones, the number of dial phones can be calculated as:
Number of dial phones = 3/5 * 3000
Number of dial phones = 1800
2. Calculate the number of digital phones:
If 2/3 of the dial phones are replaced by digital phones, the number of digital phones can be calculated as:
Number of digital phones = 2/3 * 1800
Number of digital phones = 1200
3. Calculate the total number of phones after replacement:
Since 400 additional phones are installed, the total number of phones after replacement can be calculated as:
Total number of phones = 3000 + 400
Total number of phones = 3400
4. Calculate the fraction of phones that are digital now:
Fraction of phones that are digital = Number of digital phones / Total number of phones
Fraction of phones that are digital = 1200 / 3400
Fraction of phones that are digital ≈ 0.3529
Therefore, approximately 0.3529 (or 35.29%) of the phones in Loyola Heights are digital now.